AT HOME CORP
8-K, 1997-10-22
COMPUTER PROGRAMMING, DATA PROCESSING, ETC.
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<PAGE>
 
                       SECURITIES AND EXCHANGE COMMISSION

                            WASHINGTON, D.C.  20549


                            ________________________

                                    FORM 8-K

                                CURRENT REPORT
                        PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

     DATE OF REPORT (DATE OF EARLIEST EVENT REPORTED):  October 2, 1997

                              At Home Corporation
- --------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

                                  Delaware
           -------------------------------------------------------
                (State or other jurisdiction of incorporation)

         000-22697                                  77-0408542
     -------------------                          --------------  
     (COMMISSION                                 (IRS EMPLOYER
      FILE NUMBER)                                IDENTIFICATION NO.)

               425 Broadway, Redwood City, California      94063
- --------------------------------------------------------------------------------
              (Address of principal executive offices)  (Zip code)

                                (650) 569-5000
           -------------------------------------------------------
              (Registrant's telephone number, including area code)

                                Not Applicable
           -------------------------------------------------------
         (Former name or former address, if changed since last report)
<PAGE>
 
ITEM 5.   OTHER EVENTS

          Effective October 2, 1997, the Registrant entered into a Letter
Agreement and Term Sheet with Cablevision Systems Corporation ("Cablevision"),
CSC Parent Corporation ("CSC Parent"), Comcast Corporation ("Comcast"), Cox
Enterprises, Inc. ("Cox"), Kleiner, Perkins, Caufield & Byers and Tele-
Communications, Inc. ("TCI") (the "Agreement").  The Agreement provides that
Cablevision will enter into a Master Distribution Agreement for the distribution
of the Registrant's @Home service on substantially the same terms and conditions
as TCI, Comcast and Cox.  The Agreement provides for the issuance to Cablevision
and CSC Parent of a warrant to purchase up to 7,875,784 shares of the
Registrant's Series A Common Stock at an exercise price of $.50 per share (the
"Warrant").  The Warrant is immediately exercisable, subject to the receipt of
all necessary governmental consents or approvals.  The Agreement also provided
for the issuance of a warrant to purchase up to 3,071,152 shares of the
Registrant's Series A Common Stock at an exercise price of $.50 per share under
certain conditions (the "Contingent Warrant").  The Contingent Warrant is not
immediately exercisable and will become exercisable as and to the extent certain
cable television systems are transferred from TCI and its controlled affiliates
to CSC, CSC Parent or their controlled affiliates.  Copies of the Agreement, the
related Warrant Purchase Agreement, the Warrant and the Contingent Warrant are
filed as Exhibits 10.01 through 10.04 hereto and are incorporated herein by
reference.

 
ITEM 7.     FINANCIAL STATEMENTS, PRO FORMA FINANCIAL INFORMATION 
            AND
            EXHIBITS


      (c)   Exhibits

        Exhibit Number     Exhibit
        --------------     -------
        10.01              Letter Agreement and Term Sheet among the Registrant,
                           Cablevision Systems Corporation, CSC Parent
                           Corporation, Comcast Corporation, Cox Enterprises,
                           Inc., Kleiner, Perkins, Caufield & Byers and Tele-
                           Communications, Inc., dated as of October 2, 1997

        10.02              Warrant Purchase Agreement between the Registrant and
                           Cablevision Systems Corporation, dated October 10,
                           1997

        10.03              Warrant to Purchase Shares of Series A Common Stock
                           of the Registrant issued to CSC Parent Corporation,
                           dated October 10, 1997

        10.04              Contingent Warrant to Purchase Shares of Series A
                           Common Stock of the Registrant issued to CSC Parent
                           Corporation, dated October 10, 1997

                                       2
<PAGE>
 
                                   SIGNATURES

          Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                      At Home Corporation


                                          /s/ Kenneth A. Goldman
Date:  October 21, 1997               By:_________________________
                                         Kenneth A. Goldman,
                                         Senior Vice President and
                                         Chief Financial Officer

                                       3
<PAGE>
 
                               INDEX TO EXHIBITS


        Exhibit Number     Exhibit
        --------------     -------
        10.01              Letter Agreement and Term Sheet among the Registrant,
                           Cablevision Systems Corporation, CSC Parent
                           Corporation, Comcast Corporation, Cox Enterprises,
                           Inc., Kleiner, Perkins, Caufield & Byers and Tele-
                           Communications, Inc., dated as of October 2, 1997

        10.02              Warrant Purchase Agreement between the Registrant and
                           Cablevision Systems Corporation, dated October 10,
                           1997

        10.03              Warrant to Purchase Shares of Series A Common Stock
                           of the Registrant issued to CSC Parent Corporation,
                           dated October 10, 1997

        10.04              Contingent Warrant to Purchase Shares of Series A
                           Common Stock of the Registrant issued to CSC Parent
                           Corporation, dated October 10, 1997





                                        

                                       4

<PAGE>
 
                                                                   EXHIBIT 10.01
 
                              AT HOME CORPORATION
                              425 Broadway Street
                            Redwood City, CA 94063



                                                                October 2, 1997,
                                                     as amended October 10, 1997

Cablevision Systems Corporation
CSC Parent Corporation
Comcast Corporation
Cox Enterprises, Inc.
Kleiner, Perkins, Caufield & Byers
Tele-Communications, Inc.

Dear Sirs:


     Reference is made to the term sheet (the "Term Sheet") attached hereto
regarding, among other things, the issuance and sale of certain warrants to
purchase Series A Common Stock of At Home Corporation ("@Home"), the execution
and delivery of certain instruments relating to the @Home Master Distribution
Agreement, and the waiver of certain rights under, and the amendment of certain
provisions contained in, the Stockholders Agreement (as defined below).  Unless
the context requires otherwise, capitalized terms not defined in this letter
agreement (this "Letter Agreement") or in the Term Sheet shall have the
definitions ascribed to them in the Amended and Restated Stockholders'
Agreement, dated as of July 16, 1997, among @Home, and Comcast Corporation
("Comcast"), Cox Enterprises, Inc. ("Cox"), Kleiner, Perkins, Caufield & Byers
("KPCB"), Tele-Communications, Inc. ("TCI"), and certain of their respective
subsidiaries (the "Stockholders Agreement").



     The Term Sheet sets forth the agreements of the parties in respect of the
transactions contemplated thereby.  The parties intend that the covenants and
agreements set forth in the Term Sheet will be superseded by definitive
agreements and instruments which will contain provisions incorporating and
expanding upon the agreements set forth therein, together with other provisions
customary in the case of transactions of the type described therein, and such
other provisions as are reasonable and appropriate in the context of the
transactions contemplated hereby and thereby.  Notwithstanding the foregoing,
the parties expressly acknowledge and agree that this Letter Agreement
(including the Term Sheet) constitutes a binding agreement among them, subject
to the terms and conditions set forth in this Letter Agreement and the Term
Sheet, until such definitive agreements are executed and delivered.  If such
definitive agreements are not executed and delivered within sixty (60) days from
the date of this Letter Agreement, then this Letter Agreement and the Term Sheet
(other than Section I thereof, to the extent incorporated in the Warrant
Purchase Agreement) shall be deemed to be such definitive agreements commencing
on the date hereof.  Each party hereto agrees to use its commercially reasonable
efforts to consummate the transactions contemplated by this Letter Agreement and
the Term Sheet, and the completion of such definitive agreements.
<PAGE>
 
     This Letter Agreement will be governed by, and construed in accordance
with, the laws of the State of Delaware, without regard to the conflicts of law
rules of such state.  The parties hereto agree that irreparable damage would
occur in the event any provision of the Letter Agreement or the Term Sheet was
not performed in accordance with the terms hereof or thereof, and that the
parties shall be entitled to specific performance (subject to the moving party
sustaining the applicable burden necessary to obtain such relief including as to
the inadequacy of money damages) of the terms hereof and thereof in addition to
any other remedy at law or in equity.



     Each party hereto severally represents to each of the other parties hereto
that this Letter Agreement has been duly authorized (subject, in the case of
each of @Home, CSC Parent and CSC, to the receipt of approval of the
transactions contemplated hereby by its Board of Directors), executed and
delivered by such party and constitutes the legal, valid and binding obligation
of such party and, to the extent applicable, the members of such party's
Stockholder Group (or, in the case of Cablevision Systems Corporation ("CSC"),
CSC and its Controlled Affiliates (the "CSC Stockholder Group," which term shall
be deemed to include CSC Parent Corporation ("CSC Parent"), which entity is to
become the parent corporation of CSC upon the merger (the "CSC Merger") of CSC
Parent and CSC pursuant to the Contribution and Merger Agreement, dated as of
June 6, 1997 (the "Contribution Agreement"), among TCI Communications, Inc.
("TCIC"), CSC, CSC Parent and CSC Merger Corporation)), enforceable against such
party and the applicable members of its Stockholder Group (or the CSC
Stockholder Group) in accordance with its terms, except as such enforceability
may be limited by bankruptcy, insolvency, reorganization, moratorium and similar
laws affecting the rights of creditors generally and by general principles of
equity.  (References herein to "CSC Parent" assume the consummation of the CSC
Merger; in the event that such merger is not consummated or the Contribution
Agreement is terminated, such references to CSC Parent shall be deemed to be
references to CSC.)



     In addition, (i) @Home represents and warrants to CSC and CSC Parent that
it has delivered to CSC (or, with respect to the letter agreement among @Home
and the Cable Parents relating to @Work Remote, is delivering to CSC on or
before the date of this amendment), true and complete copies of all agreements
between @Home and any member of a Stockholder Group and (ii) TCI represents and
warrants to CSC and CSC Parent that except for those agreements delivered to CSC
by @Home in accordance with clause (i) above, as of the date hereof there are no
agreements between a member of the TCI Stockholder Group, on the one hand, and a
member of any other Stockholder Group, on the other, relating to @Home;
                                                                       
provided, however, that (x) for purposes of the representations and warranties
- --------  -------                                                             
set forth in this sentence, the term "agreement" shall not include any .Com or
Promotional Agreements or any Local Cable Operator Agreements, provided that
such agreements were entered into in accordance with the terms of the
Stockholders Agreement, the Master Distribution Agreement and/or the Fourth
Amended and Restated Certificate of Incorporation of @Home (as applicable) and
(y) the parties acknowledge that @Home has not provided CSC with the letter
agreement, dated August 22, 1997, among @Home and the Cable Parents regarding
the @Work Remote service, which letter agreement shall be provided to CSC by
@Home prior to the Effective Date (as defined below).

                                      -2-
<PAGE>
 
     Each of @Home and CSC agrees to promptly provide to the other reasonable
access to its books, records, contracts and other information relating to its
business, including, but not limited to, in the case of CSC, information
concerning those of its contracts, agreements, arrangements, understandings,
investments and businesses which may form a basis for exceptions from the full
application to CSC of the Cable Parent Exclusivity Provisions.  The parties
acknowledge that CSC shall only be required to provide information pursuant to
the foregoing which is reasonably related to the transactions contemplated
hereby.  Information relating to CSC's proposed exceptions to the Cable Parent
Exclusivity Provisions shall be delivered to @Home by CSC promptly following the
date of execution of this Letter Agreement by it, and in any event not less than
one business day prior to the Effective Date (as defined below).  Confidential
information disclosed by @Home and CSC to each other shall be subject to the
terms of the Non-Disclosure Agreement, dated as of July 24, 1996, between @Home
and CSC.


     The parties agree that Section 4.6(a) of the Stockholders Agreement will be
amended to change the reference to "two Stockholders" in the second line thereof
to "three Stockholders".


     The parties agree that in the event the consideration received by TCI or
its Controlled Affiliates in connection with the initial transfer of a
Contributed System to CSC or CSC Parent consists in whole or in part of (a)
assets constituting one or more cable television systems or (b) the ownership of
securities of any entity that owns and operates one or more cable television
systems (other than securities of CSC or CSC Parent), in either case which cable
television system is a Controlled Affiliate of CSC or CSC Parent prior to such
exchange (such cable television system so transferred to TCI or its Controlled
Affiliates by CSC, CSC Parent or their Controlled Affiliates is referred to as
an "Exchanged System"), which transfer or exchange results in any such Exchanged
System becoming a Controlled Affiliate of TCI (an "Exchange"), then upon the
consummation of such Exchange, a number of Contingent Warrants equal to (x) the
number of Homes Passed of such Exchanged System as of September 30, 1997
multiplied by (y) two (subject to appropriate adjustments to give effect to any
stock splits, reverse stock splits, stock dividends, recapitalizations and the
like occurring after September 29, 1997) will be terminated and will not become
exercisable.


     CSC represents and warrants to @Home that its certification letter to
@Home, dated October 10, 1997, sets forth a true and complete list as of
September 30, 1997 and as of the date of issuance of the Warrants, of those
cable television systems of CSC, CSC Parent and their Controlled Affiliates that
are subject to sale or other transfer agreements which may result in such cable
television systems ceasing to be Controlled Affiliates of CSC or CSC Parent (the
"Subject Systems"), together with the Homes Passed of such Subject Systems as of
September 30, 1997.


     @Home covenants and agrees with CSC and CSC Parent that in the event that
@Home undertakes prior to March 31, 1998 any sale or issuance of New Capital
Stock with respect to which the CSC Stockholder Group has exercised its
preemptive rights pursuant to Section 8.1 of the Stockholders Agreement, then
@Home shall extend the period specified in Section 8.1(d) of the Stockholders
Agreement in which the CSC Stockholder Group is required to consummate such
purchase to 135 days following March 31, 1998.

                                      -3-
<PAGE>
 
  This Letter Agreement may be executed in counterparts, each of which shall be
deemed an original and all of which shall constitute one and the same
instrument.  Upon the execution of this Letter Agreement by a party hereto, this
Letter Agreement and the Term Sheet shall be the valid, binding and enforceable
agreement of such party as of the date first above written, notwithstanding the
failure of the other parties to execute and deliver this Letter Agreement at
such time; provided, however, that (i) the enforceability of this Letter
           --------  -------                                            
Agreement and the Term Sheet as to each of @Home and CSC, CSC Parent and its
Controlled Affiliates shall be subject to the condition subsequent that this
Letter Agreement and the transactions contemplated hereby be approved by the
Board of Directors of @Home and CSC, respectively, and (ii) this Letter
Agreement and the Term Sheet shall terminate and cease to be of any force and
effect in the event that (x) the requisite approvals of this Letter Agreement
and the transactions contemplated hereby by the Boards of Directors of both
@Home and CSC have not been obtained by 9:00 A.M., California time, on October
10, 1997, or (y) this Letter Agreement shall not have been executed and
delivered by all of the parties hereto by 9:00 A.M., California time, on October
10, 1997 (the date of the last to occur of such Board approvals and execution
and delivery is referred to as the "Effective Date").  If for whatever reason
the Warrants have not been issued to CSC by 5:00 P.M., New York City time, on
the Effective Date, then this Letter Agreement and the Term Sheet shall
terminate.  Termination of this Letter Agreement and the Term Sheet shall not
affect the liability of any party hereto for its breach of this Letter Agreement
or the Term Sheet occurring prior to such termination.


     Each of Comcast, Cox, KPCB and TCI acknowledges and agrees that their
execution of this Letter Agreement shall constitute the consent of their
respective Stockholder Affiliates listed in Schedule I hereto to the
transactions contemplated by this Letter Agreement.


     If the foregoing is in accordance with your understanding please indicate
your agreement by signing below, at which time this letter will constitute a
binding agreement among us.



                                    Very truly yours,



                                    AT HOME CORPORATION



                                    By:_________________________________
                                       Name:     Thomas A. Jermoluk
                                       Title:    Chairman of the Board,
                                                 President and Chief
                                                 Executive Officer

                                      -4-
<PAGE>
 
Accepted and Agreed as of
the date first above written:


CABLEVISION SYSTEMS CORPORATION

By:____________________________________
   Name:
   Title:


CSC PARENT CORPORATION

By:____________________________________
   Name:
   Title:


COX ENTERPRISES, INC.

By:____________________________________
   Name:
   Title:


COMCAST CORPORATION

By:____________________________________
   Name:
   Title:


KLEINER PERKINS CAUFIELD & BYERS

By:____________________________________

   Name:
   Title:


TELE-COMMUNICATIONS, INC.

By:____________________________________
   Name:
   Title:

                                      -5-
<PAGE>
 
                              AT HOME CORPORATION



                                 TERM SHEET



I.  ISSUANCE AND SALE OF WARRANTS TO PURCHASE @HOME SERIES A COMMON STOCK
    ---------------------------------------------------------------------


     On the Effective Date, @Home will enter into a Warrant Purchase Agreement
with CSC and CSC Parent in substantially the form attached hereto as Exhibit A
pursuant to which @Home will issue and sell, and CSC and CSC Parent will
purchase, on the Effective Date, warrants (the "Warrants") to purchase a number
of shares of the Series A Common Stock of @Home equal to the product of (x) the
number of Homes Passed of (1) CSC and CSC Parent and (2) the Contributed Systems
(as defined below), in each case including their Controlled Affiliates and
calculated as of September 30, 1997, and (y) two (subject to appropriate
adjustments to give effect to any stock splits, reverse stock splits, stock
dividends, recapitalizations and the like occurring after the date hereof and
prior to the issuance of the Warrants).  As used herein, the term "Contributed
Systems" shall mean those cable television systems owned and operated by TCI and
its Controlled Affiliates as of the date hereof which are to be transferred to
CSC, CSC Parent or their Controlled Affiliates pursuant to the Contribution
Agreement and certain other arrangements between CSC and TCI, which cable
television systems are listed in a certification letter of TCI, dated October 9,
1997, as to the Homes Passed of the Contributed Systems.  Warrants issued in
respect of Homes Passed of the Contributed Systems shall be issued as
"Contingent Warrants."  The Contingent Warrants shall not be immediately
exercisable, but shall become exercisable as and to the extent that any of the
Contributed Systems to which such Contingent Warrants relate are transferred to
CSC Parent, CSC or their Controlled Affiliates. In addition, upon the
termination of any agreement providing for the transfer of Contributed Systems
(other than by consummation thereof), the number of Contingent Warrants relating
to the Contributed Systems subject to such terminated agreement shall terminate
at such time.  All Warrants and Contingent Warrants, whether or not then
exercisable, shall terminate immediately following the close of business on the
Warrant Termination Date.


     The aggregate purchase price for the Warrants shall be $1.00, payable in
cash.  The exercise price of the Warrants shall be $.50 per share, subject to
appropriate adjustments to give effect to any stock splits, reverse stock
splits, stock dividends, recapitalizations and the like occurring after the date
hereof.  The Warrants shall be immediately exercisable; provided, however, that
                                                        --------  -------      
(i) any Contingent Warrants will not be immediately exercisable and will become
exercisable as provided above and (ii) any such exercise shall be subject to the
receipt of all necessary governmental consents or approvals or the expiration of
any applicable waiting period under the HSR Act.  All outstanding but
unexercised Warrants will expire and cease to be exercisable on the fifth
anniversary of the initial issuance of the Warrants (the "Warrant Termination
Date"); provided, however, that in the event that CSC has been unable to
        --------  -------                                               
exercise the Warrants prior to the Warrant Termination Date because of the
failure to receive a governmental consent or approval or the failure of the
waiting period under the HSR Act to have expired or have terminated (despite its
and @Home's continuing use of commercially reasonable efforts to obtain such
consent or approval or the expiration or termination of such waiting period),
then CSC or CSC Parent, as the case may be, shall have the right to acquire upon
<PAGE>
 
exercise of any remaining Warrants on the Warrant Termination Date (other than
any Contingent Warrants which are not then exercisable) shares of a class or
series of non-voting, transferable, equity securities of @Home that are
convertible at any time (subject to the prior receipt of any required
governmental consents or approvals or the expiration or termination of any
waiting period under the HSR Act) into the number of shares of Series A Common
Stock that CSC or CSC Parent would have obtained upon exercise of the remaining
Warrants (other than any such unexercisable Contingent Warrants) immediately
prior thereto and upon payment of the aggregate exercise price that would have
been so payable; and the parties hereto agree to take such steps as may be
reasonably necessary to effect the creation, authorization and issuance of such
securities (such securities and the Warrant Shares are collectively referred to
as the "Warrant Securities").


II.  MASTER DISTRIBUTION AGREEMENT.
     ----------------------------- 


     CSC, CSC Parent, @Home and each Cable Parent will enter into an instrument
(the "MDA Instrument") pursuant to which CSC and CSC Parent shall become parties
to the Master Distribution Agreement and will become entitled to all rights, and
subject to all obligations, thereunder, except as specifically provided herein.
The MDA Instrument will provide that CSC (and any other Controlled Affiliate of
CSC Parent which conducts the cable distribution business of CSC Parent) will be
a "Cable Parent" and that CSC Parent will be a "Parent," in each case for all
purposes of the Master Distribution Agreement, and shall have the rights,
benefits and obligations of a "Cable Parent" and a "Parent," respectively, as
provided therein and in the Local Cable Operator Agreement (the "LCO
Agreement"), except to the extent a provision of the Master Distribution
Agreement or the LCO Agreement refers to specific Cable Parents or Parents
(including, but not limited to, Sections 8 and 10 of the Master Distribution
Agreement and Section 4(c) of the LCO Agreement); provided, that if all of the
                                                  --------                    
cable distribution business conducted, directly or indirectly, by CSC is
contributed to a subsidiary of CSC, then such subsidiary shall replace CSC as a
"Cable Parent", and CSC or CSC Parent (whichever corporation is the parent
entity of the CSC Stockholder Group) shall be a "Parent" for purposes of the
Master Distribution Agreement.  In addition, CSC (with respect to periods prior
to the CSC Merger ) and CSC Parent (with respect to periods subsequent to the
CSC Merger) shall provide the same undertakings and covenants as each of TCI,
CEI and Comcast provided as a "Parent" pursuant to the Master Distribution
Agreement (including, without limitation, under Section 17 thereof).



     For purposes of clarification, (i) CSC and CSC Parent shall be entitled to
the benefits of the MFN (as defined in the Master Distribution Agreement)
(including, but not limited to, the right to co-brand the @Home Services (as
defined in the Master Distribution Agreement) with @Home) and roll-out
priorities on the same basis as all other Cable Parents and (ii) neither CSC nor
CSC Parent shall be entitled to (x) become a "High C" or a "Triggering Cable
Parent" for purposes of Section 8 of the Master Distribution Agreement, (y)
terminate the Cable Parent Exclusivity Provisions upon a TCI Change in Control
or (z) terminate the Cable Parent Exclusivity Provisions as to itself prior to
the earlier of (1) June 4, 2002 and (2) the date of the effectiveness of any
change in law, statute, or regulation or the entering of any adverse judicial
decision or injunction or other action, in each case which materially impairs
the enforceability (in accordance with their respective terms) of any of the
Cable Parent Exclusivity Provisions, 
<PAGE>
 
@Home Exclusivity Provisions, MFN Provisions or the Content Tag-Along Right (as
each such term is defined in the Master Distribution Agreement). Notwithstanding
the limitation of clauses (x) and (y) of clause (ii) above, in the event either
CCI or Comcast Cable elects to terminate the Cable Parent Exclusivity Provisions
pursuant to Sections 8 or 10 of the Master Distribution Agreement, or the Cable
Parent Exclusivity Provisions are otherwise terminated (or become terminable) in
accordance with their terms as to all other Cable Parents, such provisions may
be terminated by CSC (with respect to itself) at the same time as such
provisions terminate (or become terminable) as to the other Cable Parents;
provided, however, that the Cable Parent Exclusivity Provisions shall not be
- --------  -------                
deemed terminable as a result of Comcast or CCI having the right to terminate
the Cable Parent Exclusivity Provisions pursuant to Sections 8 or 10 of the
Master Distribution Agreement until such time as Comcast or CCI, as the case may
be, terminates the Cable Parent Exclusivity Provisions in accordance with the
terms of said Sections 8 or 10. In addition, CSC and CSC Parent acknowledge and
agree that notwithstanding their obtaining of rights on the same basis as the
other Cable Parents (except as otherwise provided herein) under the Master
Distribution Agreement, neither CSC nor CSC Parent shall be entitled to any
rights equivalent to those granted to the Comcast Stockholder Group pursuant to
Section 6 of the Master Distribution Agreement and the exercise by Comcast of
the Comcast Nonexclusive Right pursuant to said Section 6 shall not affect the
obligations of CSC or CSC Parent or any other Cable Parent (other than the
members of the Comcast Stockholder Group) under the Cable Parent Exclusivity
Provisions.


     CSC and CSC Parent hereby acknowledge and agree that none of CSC, CSC
Parent or any other member of the CSC Stockholder Group shall be an Either E
Cable Parent for purposes of the making of the Required Either E Cable Parent
Election pursuant to Section 4(c) of the LCO Agreement.  In the event of a
Required Either E Cable Parent Election (as defined in the LCO Agreement) to
increase the revenue percentage split to @Home, the percentage split to @Home in
all then existing LCO Agreements between @Home and CSC and its Controlled
Affiliates shall not be increased on the date of the Required Either E Cable
Parent Election (the "Split Change Date") but any LCO Agreements entered into by
CSC and its Controlled Affiliates subsequent to the Split Change Date (including
any subsequent renewals of LCO Agreements in effect on such date) shall be
subject to and shall incorporate such increased percentage split.  Each Cable
Parent acknowledges and agrees that the application of the foregoing to CSC in
respect of increases in the percentage split to @Home arising from a Required
Either E Cable Parent Election shall not entitle such Cable Parent to assert its
MFN rights with respect to the fact that such changed revenue split is not
immediately applicable to CSC.


     The MDA Instrument shall have such other terms and provisions as the
parties may agree, and CSC and CSC Parent shall be entitled to reasonable
exceptions to the full application of the Cable Parent Exclusivity Provisions
with respect to certain investments and activities as they currently have or are
engaged in (on a basis substantially similar to that upon which the Cable
Parents excluded such investments and activities in connection with the
execution of the Term Sheet, dated June 4, 1996, among the parties thereto).
<PAGE>
 
III.  REGISTRATION RIGHTS.
      ------------------- 


     The currently outstanding @Home Registration Rights Agreement shall be
amended to provide CSC Parent with registration rights with respect to the
shares of Series A Common Stock issuable upon exercise of the Warrants.  CSC
Parent shall be entitled to two (2) Demand Registrations (as defined therein)
and other registration rights which are pari passu with those provided to TCI
                                        ---- -----                           
(other than the Special Registration Right (as defined therein)), Cox and
Comcast.


IV.  STOCKHOLDERS AGREEMENT AMENDMENT AND WAIVER.
     ------------------------------------------- 


     The parties will enter into an Amended and Restated Stockholders Agreement
amending and restating the provisions of the existing Stockholders Agreement, as
amended hereby.


1.  Waiver of Certain Provisions of the Stockholders Agreement.
    ---------------------------------------------------------- 

Pre-Emptive Rights:                 Each Eligible Stockholder waives (i) any
                                    rights under Article 8 of the Stockholders
                                    Agreement to receive any notice of the
                                    proposed issuance and sale by @Home of the
                                    Warrants or the Warrant Securities; (ii) any
                                    rights under Article 8 of the Stockholders
                                    Agreement to acquire from @Home a pro rata
                                    portion of the Warrants or the Warrant
                                    Securities and/or other securities of @Home
                                    sufficient to maintain its proportional
                                    interest in @Home after giving effect to the
                                    issuance of the Warrants; (iii) any rights
                                    to acquire "New Capital Stock" as defined in
                                    the Stockholders Agreement with respect to
                                    the issuance of the Warrants or the Warrants
                                    Securities; and (iv) any right of first
                                    refusal or other rights granted to it under
                                    the Stockholders Agreement applicable to the
                                    issuance of the Warrants or the Warrant
                                    Securities. The issuance of the Warrant
                                    Securities upon exercise of Warrants shall
                                    not result in any Stockholder becoming
                                    entitled to exercise any preemptive rights
                                    in respect thereof.


2.  Amendments to Stockholder Agreement.
    ----------------------------------- 

Addition of CSC                     In connection with their acquisition of the 
Stockholder Group:                  Warrants from @Home, CSC Parent, CSC and the
                                    wholly owned subsidiary of CSC which holds
                                    the Warrants ("CSC Sub") would become
                                    parties to the Stockholders Agreement and
                                    would be entitled to all of the rights and
                                    benefits, and would be subject to all of the
                                    obligations, thereunder on the same basis as
                                    the Comcast Stockholder Group, the Cox
                                    Stockholder Group and the TCI Stockholder
                                    Group, except as otherwise specifically
                                    provided herein.
<PAGE>
 
                                    Without limiting the generality of the
                                    foregoing, the parties acknowledge and agree
                                    that the following matters will be amended
                                    in connection with the consummation of the
                                    transactions contemplated hereby:
 
 
                                    (a)  The definition of "Company Securities"
                                         will be amended to provide that the
                                         Warrants (which, for purposes of this
                                         paragraph (a), shall be deemed to
                                         include any securities which were
                                         originally issued as Contingent
                                         Warrants which have, as of the
                                         applicable date of determination,
                                         become exercisable as a result of the
                                         transfer to CSC, CSC Parent or their
                                         Controlled Affiliates of the
                                         Contributed Systems with respect to
                                         which such Contingent Warrant related),
                                         the Warrant Securities and any CSC
                                         Contingent Securities (as defined
                                         below) will be deemed Company
                                         Securities notwithstanding the fact
                                         that the Warrant Securities issuable
                                         upon the exercise of the Warrants
                                         would, and the issuance of securities
                                         upon exercise of any CSC Contingent
                                         Securities may, require the payment of
                                         additional consideration; provided,
                                                                   --------
                                         however, that for purposes of any
                                         -------
                                         determination of CSC's proportionate
                                         equity ownership of @Home (e.g., for
                                         purposes of calculating the amount of
                                         New Capital Stock purchasable by CSC
                                         upon exercise of its preemptive rights,
                                         the number of shares with respect to
                                         which it is entitled to participate
                                         pursuant to the exercise of its Tag-
                                         Along Right or the number of shares it
                                         is entitled to purchase pursuant to the
                                         Right of First Offer), the CSC
                                         Contingent Securities will be deemed
                                         issued and outstanding Company
                                         Securities, subject to the following:
 
 
 
                                         (1)  Preemptive Rights.  Any 
                                              -----------------
                                              securities which become
                                              purchasable by the CSC Stockholder
                                              Group (x) pursuant to the exercise
                                              of their preemptive rights and (y)
                                              which are based upon the ownership
                                              of CSC Contingent Securities by
                                              the CSC Stockholder Group, and
                                              which the CSC Stockholder Group
                                              elects to purchase, shall be
                                              issued to CSC Sub as contingent
                                              securities and shall not become
                                              vested or exercisable until the
                                              underlying CSC Contingent
                                              Securities become exercisable. As
                                              used herein, the term "CSC
                                              Contingent 
<PAGE>
 
                                              Securities" (i) means, (x) the
                                              Contingent Warrants and (y) any
                                              securities issuable to CSC on the
                                              basis of its ownership of
                                              Contingent Warrants, which, as of
                                              the date of determination, are, in
                                              the case of clauses (x) or (y),
                                              not then exercisable because the
                                              transfer to CSC or CSC Parent of
                                              the Contributed System in respect
                                              of which such Contingent Warrant
                                              or other security was originally
                                              issued has not then been
                                              completed, and (ii) includes any
                                              other securities issued or
                                              transferred to CSC or CSC Parent
                                              hereunder in respect of other "CSC
                                              Contingent Securities" which are
                                              similarly unexercisable or
                                              unvested pending completion of
                                              such a transfer. If the CSC
                                              Stockholder Group seeks to
                                              purchase less than the full amount
                                              of securities it could acquire as
                                              a result of the exercise of its
                                              preemptive rights, the securities
                                              so acquired shall be deemed to
                                              have been acquired in respect of
                                              securities of @Home owned by the
                                              CSC Stockholder Group that are not
                                              CSC Contingent Securities, up to
                                              the amount of securities that
                                              could have been acquired solely in
                                              respect of such securities (other
                                              than any CSC Contingent
                                              Securities). Upon the expiration
                                              or termination of any Contingent
                                              Warrants, CSC shall promptly give
                                              @Home notice of such expiration or
                                              termination and specify those CSC
                                              Contingent Securities, if any,
                                              which were issued to a member of
                                              CSC Stockholder Group in respect
                                              of such expired or terminated
                                              Contingent Warrants pursuant to
                                              the exercise of such pre-emptive
                                              rights, which notice shall also
                                              constitute an offer by the CSC
                                              Stockholder Group to sell up to
                                              such amount of such CSC Contingent
                                              Securities to @Home or its
                                              designee at a price equal to the
                                              amount the CSC Stockholder Group
                                              originally paid to @Home in the
                                              original purchase of the CSC
                                              Contingent Securities to be sold
                                              back to @Home, which offer shall
                                              remain open for a period of 60
                                              days following the delivery of
                                              such notice to @Home. @Home shall
                                              then promptly (and in any event
                                              not later than the fifth business
                                              day following its receipt of such
<PAGE>
 
                                              offer notice) notify each
                                              Stockholder which purchased
                                              securities in the same transaction
                                              in which the CSC Stockholder Group
                                              purchased such CSC Contingent
                                              Securities of such expiration or
                                              termination, which notice will
                                              constitute an offer by @Home
                                              (subject to the consummation of
                                              its corresponding purchase of such
                                              securities from the CSC
                                              Stockholder Group) to sell to each
                                              such Stockholder up to its Pro
                                              Rata Share (as defined below) of
                                              such CSC Contingent Securities, at
                                              the same price at which @Home may
                                              purchase such securities from the
                                              CSC Stockholder Group. Upon a
                                              Stockholder's written acceptance
                                              of such offer (which acceptance
                                              shall be delivered to @Home within
                                              45 days of such Stockholder's
                                              receipt of such offer notice),
                                              @Home will accept the CSC
                                              Stockholder Group's offer with
                                              respect to a like number of
                                              securities and purchase such
                                              securities from the CSC
                                              Stockholder Group. @Home will then
                                              notify the CSC Stockholder Group
                                              within such 60 day period referred
                                              to above of the number of CSC
                                              Contingent Securities @Home will
                                              purchase from the CSC Stockholder
                                              Group, if any. @Home and such
                                              accepting Stockholder will then
                                              consummate the sale of such
                                              securities as promptly as
                                              practicable thereafter, and upon
                                              such consummation such securities
                                              shall be fully vested and
                                              exercisable. The foregoing
                                              purchases and sales shall be
                                              subject to the terms and
                                              conditions set forth in Section
                                              11.9 of the Stockholders
                                              Agreement. As used herein, a
                                              Stockholder's Pro Rata Share shall
                                              be an amount of Company Securities
                                              equal to the product of (x) the
                                              total number of CSC Contingent
                                              Securities that the CSC
                                              Stockholder Group is then required
                                              to offer to sell to @Home and (y)
                                              a fraction, the numerator of which
                                              is the number of Company
                                              Securities which such Eligible
                                              Stockholder offered to purchase in
                                              the original exercise of
                                              preemptive rights, and the
                                              denominator of which is the number
                                              of Company Securities which all
                                              Eligible Stockholders (other than
                                              the members of the CSC Stockholder
                                              Group) requested to 
<PAGE>
 
                                              purchase in such original exercise
                                              of preemptive rights.
 
 
 
                                         (2)  Purchase or Sale of Company
                                              ---------------------------
                                              Securities Pursuant to the Tag-
                                              ------------------------------
                                              Along Right, Drag-Along Right or
                                              --------------------------------
                                              Right of First Offer. In the event
                                              --------------------
                                              the CSC Stockholder Group (a)
                                              becomes (i) entitled to sell any
                                              Company Securities pursuant to its
                                              exercise of the Tag-Along Right,
                                              or (ii) obligated to sell pursuant
                                              to the Drag-Along Right, or (b)
                                              proposes to transfer Company
                                              Securities in a transaction which
                                              is subject to the other
                                              Stockholders' Right of First Offer
                                              (any such transaction, a "Sale
                                              Transaction"), it shall be
                                              entitled to include the securities
                                              of @Home which it owns, including
                                              its Warrants and CSC Contingent
                                              Securities, on the same pro rata
                                              basis as the other Stockholders
                                              are entitled to include their
                                              Company Securities, in any such
                                              sale; provided, that any agreement
                                                    --------
                                              in respect of such sale will
                                              provide that in the event any CSC
                                              Contingent Securities terminate or
                                              expire prior to such securities
                                              becoming vested or exercisable,
                                              the CSC Stockholder Group shall be
                                              required to return to the buyer
                                              thereof (including any ROFO
                                              Electing Stockholder) the
                                              consideration received by it in
                                              respect of such CSC Contingent
                                              Securities and the Stockholders
                                              selling securities in such
                                              transaction and the buyer shall
                                              enter into reasonable arrangements
                                              designed to assure that the buyer
                                              will have the right to acquire
                                              from such Stockholders the same
                                              amount of Company Securities that
                                              were covered by such terminated or
                                              expired CSC Contingent Securities
                                              for an aggregate consideration
                                              equal to the consideration
                                              returned to the CSC Stockholder
                                              Group. If the CSC Stockholder
                                              Group seeks to sell less than the
                                              full amount of securities it could
                                              sell in such Sale Transaction, the
                                              securities so sold shall be deemed
                                              to have been sold 
<PAGE>
 
                                              in respect of its securities of
                                              @Home owned by the CSC Stockholder
                                              Group that are not CSC Contingent
                                              Securities, up to the amount of
                                              securities that could have been
                                              sold solely in respect of such
                                              securities other than CSC
                                              Contingent Securities.
 
 
 
                                              In the event that the CSC
                                              Stockholder Group purchases
                                              Company Securities from another
                                              Stockholder Group pursuant to its
                                              exercise of the Right of First
                                              Offer and its participation in
                                              such purchase was based, in part,
                                              on the CSC Stockholder Group's
                                              ownership of CSC Contingent
                                              Securities and any CSC Contingent
                                              Securities are later terminated or
                                              expire prior to such securities
                                              becoming vested or exercisable,
                                              the CSC Stockholder Group shall be
                                              required to offer to sell, at the
                                              same price or other consideration
                                              as the CSC Stockholder Group
                                              originally paid in respect of such
                                              Company Securities so purchased,
                                              to each other Stockholder which
                                              purchased Company Securities in
                                              such transaction a number of
                                              Company Securities equal to the
                                              product of (x) a fraction, the
                                              numerator of which is the number
                                              of Company Securities such
                                              Stockholder offered to purchase in
                                              such original transaction and the
                                              denominator of which is the number
                                              of Company Securities offered to
                                              be purchased by all Stockholders
                                              (other than the members of the CSC
                                              Stockholder Group) in such
                                              original transaction and (y) the
                                              difference between (i) the number
                                              of Company Securities purchased by
                                              the CSC Stockholder Group and (ii)
                                              the number of Company Securities
                                              the CSC Stockholder Group would
                                              have been entitled to purchase had
                                              the CSC Contingent Securities
                                              which terminated or expired not
                                              been included in its ownership of
                                              Company Securities at the time the
                                              amount purchasable by it was
                                              determined. In this regard, if the
                                              CSC Stockholder Group seeks to
                                              purchase less than the full amount
                                              of securities it could purchase
                                              pursuant to such Right of First
                                              Offer, the securities so purchased
                                              by it shall be deemed to have been
                                              purchased in respect of its
                                              securities of @Home owned by the
                                              CSC Stockholder Group that are not
                                              CSC Contingent Securities up to
                                              the amount of securities that
                                              could have been purchased 
<PAGE>
 
                                              solely in respect of such
                                              securities other than CSC
                                              Contingent Securities.
 
 
 
                                              In addition, appropriate changes
                                              to reflect the foregoing concepts
                                              will be made where reasonably
                                              necessary in the Stockholders
                                              Agreement, including but not
                                              limited to, in the definition of
                                              "Attributable Shares."
 
 
 
                                    (b)  The CSC Stockholder Group will be added
                                         to the definition of Eligible
                                         Stockholder Amount and will have an
                                         initial Eligible Stockholder Amount
                                         equal to 25% of the number of shares of
                                         Series A Common Stock subject to
                                         issuance upon exercise of the Warrants
                                         other than Contingent Warrants, with
                                         such amount to be adjusted from time to
                                         time to reflect the vesting of
                                         Contingent Warrants, and
                                         notwithstanding in each case that the
                                         exercise price of the Warrants has not
                                         been paid.
 
 
 
                                    (c)  CSC Sub shall be deemed an "Exclusive
                                         Stockholder" so long as CSC or CSC
                                         Parent remains in compliance with the
                                         Cable Parent Exclusivity Provisions
                                         from and after the date hereof.
 
 
 
                                    (d)  Appropriate changes and additions will
                                         be made to the definitions of "Cable
                                         Parent," "Parent," "Stockholder,"
                                         "Stockholder Group" and "CSC
                                         Stockholder Group" together with such
                                         other changes as are necessary or
                                         appropriate in light of CSC, CSC Parent
                                         and their Controlled Affiliates being
                                         parties to the Stockholder Agreement on
                                         the basis set forth herein.



Transfer Provisions:                The Warrants and the Warrant Securities
                                    (which shall be deemed "Company Securities"
                                    for purposes of the Stockholders Agreement)
                                    issued to the CSC Stockholder Group shall be
                                    subject in all respects to the Transfer
                                    restrictions set forth in Article 4 of the
                                    Stockholders Agreement and CSC Sub shall be
                                    a Stockholder thereunder and shall have full
                                    rights in accordance therewith (as modified
                                    hereby with respect to its rights in respect
                                    of Contingent Warrants) to purchase Company
                                    Securities from another Stockholder Group
                                    pursuant to Section 4.3 and 4.4 thereof.
                                    Notwithstanding the foregoing, in the event
                                    that CSC is unable to exercise all of the
                                    Warrants for Series A Common Stock and
                                    exercises Warrants on the Warrant
                                    Termination Date for 
<PAGE>
 
                                    other securities as provided above, CSC
                                    shall be entitled to exercise such Warrants
                                    and sell such Warrant Securities (and any
                                    underlying securities) issued in respect
                                    thereof in a registered public offering
                                    having wide distribution, without compliance
                                    with the provisions of Section 4.3 or 4.4 of
                                    the Stockholders Agreement, during the six-
                                    month period following the Warrant
                                    Termination Date.


Board Representation:               During the period subsequent to the @Home
                                    Board's approval of the Letter Agreement and
                                    the Warrant Closing, @Home shall cause one
                                    person designated by CSC to be permitted to
                                    attend (only as an observer) meetings of
                                    @Home's Board of Directors, subject to
                                    agreements to maintain confidential
                                    information, the right of the Board to
                                    exclude the observer from attorney-client
                                    privileged portions of meetings and the
                                    observer's compliance with @Home's policies
                                    with respect to insider trading. Each
                                    Stockholder and @Home will agree (i) to take
                                    such commercially reasonable actions as are
                                    required to cause to be appointed to the
                                    Board of @Home (as an Additional Director
                                    (as defined in the Charter)) one person
                                    designated by CSC Parent (the "CSC
                                    Designee") upon receipt from CSC following
                                    the issuance of the Warrants of a written
                                    notice that it wishes to have a CSC Designee
                                    so appointed and that such appointment does
                                    not violate any applicable federal laws and
                                    (ii) thereafter to vote those voting
                                    securities beneficially owned by it in favor
                                    of the election of the CSC Designee for so
                                    long as CSC Parent beneficially owns at
                                    least 5,000,000 shares of Common Stock,
                                    subject to appropriate adjustments to give
                                    effect to any stock splits, reverse stock
                                    splits, stock dividends, recapitalizations
                                    and the like occurring after the date hereof
                                    (the "CSC Stock Amount"), but only if CSC
                                    has not indicated its wish to cease to have
                                    a CSC Designee serve on the Board of @Home.
                                    The provisions of Section 3.4(b) of the
                                    Stockholders Agreement will be applicable to
                                    CSC Parent with respect to the CSC Designee
                                    in the event that CSC Parent ceases to
                                    beneficially own the CSC Stock Amount. CSC
                                    and CSC Parent hereby acknowledge and agree
                                    that (a) CSC shall not be entitled under the
                                    Letter Agreement and Term Sheet to designate
                                    or appoint any Person as a Series B Common
                                    Stock Director of @Home, (b) the right of
                                    CSC to designate an observer to the Board of
                                    @Home shall terminate upon the initial
                                    appointment of the CSC Designee to the Board
                                    of @Home and (c) CSC's right to a Board
                                    observer and to have the CSC Designee
                                    appointed or elected to the @Home Board as
                                    an Additional Director shall be in lieu of
                                    any right CSC or CSC Parent may have under
                                    the Letter 
<PAGE>
 
                                    Agreement and Term Sheet (as a Stockholder
                                    entitled to the same rights and subject to
                                    the same obligations as each of Comcast, Cox
                                    and TCI under the Stockholders Agreement,
                                    except as provided herein) to elect, appoint
                                    or designate any Person to be a Series B
                                    Common Stock Director. Each of TCI and CSC
                                    hereby represents and warrants (individually
                                    and not jointly) to each of Cox, Comcast and
                                    KPCB that, as of the date hereof, there does
                                    not exist any binding agreement between TCI
                                    and its Controlled Affiliates, on the one
                                    hand, and CSC and its Controlled Affiliates,
                                    on the other, which obligates TCI to elect
                                    or appoint to the Board of Directors of
                                    @Home any officer, director or employee of
                                    CSC or its Controlled Affiliates as a Series
                                    B Common Stock Director; provided, however,
                                                             -----------------
                                    that nothing herein contained shall be
                                    deemed to restrict, limit or otherwise
                                    encumber, directly or indirectly, the right
                                    of TCI to elect or appoint as its
                                    Stockholder Designees in accordance with
                                    Section 3.3 of the Stockholders Agreement
                                    such Persons as it shall determine in its
                                    sole discretion, and TCI hereby reserves the
                                    right, in its sole discretion and without
                                    consultation with any other Stockholder
                                    Group, to designate as its Stockholder
                                    Designees and to appoint or elect as Series
                                    B Common Stock Directors (but subject to the
                                    provisions of Section 3.3 of the
                                    Stockholders Agreement) such Persons as it
                                    shall determine and to enter into agreements
                                    with CSC or any other entity with respect to
                                    the same.


Deemed Transfer:                    The provisions of Article 5 of the
                                    Stockholders Agreement will be amended to
                                    provide that (i) as and to the extent
                                    Contributed Systems are transferred from the
                                    TCI Stockholder Group to the CSC Stockholder
                                    Group, the number of Base Homes Passed of
                                    TCI and its Controlled Affiliates shall be
                                    reduced by the number of Homes Passed of
                                    such Contributed Systems (the "Contributed
                                    Homes Passed") and (ii) the number of Base
                                    Homes Passed of CSC, CSC Parent and their
                                    Controlled Affiliates will be equal to the
                                    number of Homes Passed of CSC and its
                                    Controlled Affiliates used for purposes of
                                    the determination of the number of Warrants
                                    (other than the Contingent Warrants)
                                    issuable to CSC Sub, which number shall be
                                    increased from time to time upon any
                                    transfer of Contributed Systems to CSC, CSC
                                    Parent or their Controlled Affiliates. For
                                    purposes of Article V, the "Total Shares" of
                                    CSC Sub shall be the number of shares
                                    issuable upon exercise of the Warrants
                                    issuable to it pursuant to the Warrant
                                    Purchase Agreement (including Contingent
                                    Warrants), as reduced from time to time as
                                    necessary to reflect the termination of
                                    Contingent Warrants occurring upon the
                                    termination of 
<PAGE>
 
                                    agreements or arrangements providing for the
                                    transfer of Contributed Systems. Such
                                    amendment will effect corresponding changes
                                    to Schedule II to the Stockholders
                                    Agreement.


Controlled Affiliates:              For purposes of the Stockholders Agreement,
                                    the Master Distribution Agreement, the MDA
                                    Instrument, the Registration Rights
                                    Agreement and the LCO Agreement, no member
                                    of the CSC Stockholder Group shall be deemed
                                    to be a Controlled Affiliate of TCI or any
                                    member of the TCI Stockholder Group.


Covenant of Stockholders:           In the event that the exercise of the
                                    Warrants requires the approval of the
                                    stockholders of @Home, each of @Home,
                                    Comcast, Cox, KPCB and TCI agrees that such
                                    approval shall be deemed an action required
                                    to be taken pursuant to the Stockholders
                                    Agreement and that each such person shall
                                    take the actions required of it pursuant to
                                    Section 3.1 of the Stockholders Agreement in
                                    order to obtain any such approval.


Other:                              Without limitation of the foregoing, CSC and
                                    CSC Parent shall be entitled to (and shall
                                    be obligated with respect to) the preemptive
                                    rights under Article 8, the Rights of First
                                    Offer under Sections 4.3 and 4.4, the Tag
                                    Along Rights under Section 4.5, the Drag-
                                    Along Rights under Section 4.6 and the
                                    Deemed Transfer provisions of Article V of
                                    the Stockholders Agreement, in each case on
                                    the same basis as the other Stockholder
                                    Groups and to the extent required by the
                                    terms of such provision, except as otherwise
                                    provided herein.
<PAGE>
 
                                   Exhibit A



                     [Form of Warrant Purchase Agreement]
<PAGE>
 
                                 SCHEDULE I
                                 ----------



                            STOCKHOLDER AFFILIATES
                            ----------------------



TCI
- ---
TCI Internet Services, Inc.
TCI Communications, Inc.
TCI Cable Investments Inc.
TCI.NET, Inc.


KPCB
- ----
KPCB Information Sciences Zaibatsu Fund II
Kleiner, Perkins, Caufield & Byers VII
James Clark


Comcast
- -------
Comcast Cable Communications, Inc.
Comcast On-line Communications, Inc.



Cox
- ---
Cox Communications, Inc.

<PAGE>
 
                                                                   EXHIBIT 10.02



                              At Home Corporation
                                  425 Broadway
                             Redwood City, CA 94063

                                                                October 10, 1997


To: Cablevision Systems Corporation



                        Re:  Warrant Purchase Agreement
                             --------------------------

Ladies and Gentlemen:

     Reference is made to that certain Letter Agreement and Term Sheet, dated as
of October 2, 1997, as amended on October 10, 1997, and as further amended from
time to time (the "TERM SHEET"), among At Home Corporation, a Delaware
corporation (the "COMPANY"), Cablevision Systems Corporation ("CSC"), CSC Parent
Corporation, Cox Enterprises, Inc., Comcast Corporation, Kleiner Perkins
Caufield & Byers, and Tele-Communications, Inc., with respect to the
distribution of certain @Home services by CSC and its affiliates and related
matters.

     In connection with the Term Sheet, the Company has agreed to grant certain
warrants and provide certain rights to CSC, as described below.

     1.   Purchase and Sale of Warrants; Definitions.
          ------------------------------------------ 

                1.1  Purchase and Sale of Warrant. Subject to the terms and
                     ----------------------------     
conditions of this Warrant Purchase Agreement (this "AGREEMENT"), the Company
agrees to issue to CSC, and CSC agrees to accept from the Company, on the date
of this Agreement (or such other date as the parties hereto may agree) (the
"WARRANT CLOSING"), a warrant in the form attached hereto as Exhibit A (the
                                                             ---------    
"WARRANT") to purchase 7,875,784 shares of Series A Common Stock of the Company
(subject to appropriate adjustment to give effect to any stock splits, reverse
stock splits, stock dividends, recapitalizations and the like occurring after
September 29, 1997 and prior to the Warrant Closing).

                1.2  Purchase and Sale of Contingent Warrant.  Subject to the
                     ---------------------------------------     
terms and conditions of this Agreement, the Company agrees to issue to CSC, and
CSC agrees to accept from the Company, at the Warrant Closing, a warrant in the
form attached hereto as Exhibit B and subject to the provisions of this
                        ---------      
paragraph, to purchase 3,071,152 shares of the Series A Common Stock of the
Company (subject to appropriate adjustment to give effect to any stock splits,
reverse stock splits, stock dividends, recapitalizations and the like occurring
after September 29, 1997 and prior to the Warrant Closing) (the
<PAGE>
 
"CONTINGENT WARRANT", and collectively with the Warrant, the "WARRANTS");
provided, that the Contingent Warrant shall become exercisable and shall be
- --------                                                                   
terminable as provided therein.

                1.3  Exercise Price.  The Warrants shall have an exercise price
                     --------------    
of fifty cents ($0.50) per share (subject to appropriate adjustment to give
effect to any stock splits, reverse stock splits, stock dividends,
recapitalizations and the like occurring after September 29, 1997 and prior to
the Warrant Closing).

     2.  Representations, Warranties and Covenants of the Company.  The Company
         --------------------------------------------------------              
hereby represents and warrants to, and covenants with, CSC as of the date hereof
as follows:

                2.1  Authorization.  The Company has full power and authority to
                     ------------- 
execute, deliver and perform its obligations under this Agreement and the
Warrants. All corporate action on the part of the Company necessary for the
authorization, execution and delivery of this Agreement and the Warrants and the
performance of all obligations of the Company hereunder and thereunder has been
taken. The execution and delivery of this Agreement and the Warrants and the
performance of all obligations of the Company hereunder and thereunder were
approved by the Company's Board of Directors on October 7, 1997. This Agreement
and the Warrants are valid and legally binding obligations of the Company,
enforceable against it in accordance with their terms.

                2.2  No Conflict.  The execution, delivery and performance of
                     -----------     
this Agreement and the Warrants and the consummation of each of the transactions
contemplated hereby and thereby do not and will not (a) conflict with or result
in a breach of the terms, conditions or provisions of, (b) with or without
notice or lapse of time or both, constitute a default under, (c) result in the
creation of any lien, security interest, charge or encumbrance upon the
Company's capital stock or assets pursuant to, (d) with or without notice or
lapse of time or both, give any third party the right to accelerate, cancel or
terminate any obligation under, (e) result in a violation of, or (f) require any
order, qualification, waiver, permit, authorization, consent, approval,
exemption or other action by or from, or any registration, notice, declaration,
application or filing to or with, any court or administrative or governmental
body or any other person or entity pursuant to (i) the Certificate of
Incorporation or Bylaws of the Company, (ii) any agreement to which the Company
is a party or is bound or to which its assets are subject or (iii) any law,
statute, rule or regulation to which the Company is subject; provided, however,
                                                             --------  ------- 
that with respect to clause (f) of this Section 2.2, no representation or
warranty is made as to any such requirements applicable to the Company as a
result of the specific legal or regulatory status of CSC (including without
limitation any agreements between CSC or its affiliates and any local or
municipal government related to the provision of cable television services
within a local area) or as a result of any other facts that specifically relate
to CSC, any business in which CSC has engaged or proposes to engage or any

                                       2
<PAGE>
 
financing arrangements or transactions entered into or proposed to be entered
into by or on behalf of CSC and provided, further, that no representation or
                                --------  -------                           
warranty is made with respect to the application of the Hart-Scott-Rodino
Antitrust Improvements Act of 1976, as amended (the "HSR ACT"), to the exercise
of the Warrants.

                2.3  Valid Issuance of Warrants and Warrant Stock.  The
                     --------------------------------------------     
Warrants, when issued, sold and delivered in accordance with the terms of this
Agreement to CSC, will be duly authorized and validly issued and will be issued
in compliance with all federal and state securities laws. The shares issuable
upon exercise of the Warrants (the "WARRANT STOCK") have been duly and validly
reserved for issuance and, upon issuance in accordance with the terms of the
Warrants, will be duly authorized, validly issued, fully paid and nonassessable
and, assuming no distribution of the Warrants by CSC or CSC Parent, will be
issued in compliance with all federal and state securities laws.

                2.4  Valid Existence and Capitalization.  The Company is duly
                     ----------------------------------                      
incorporated, validly existing and in good standing under the laws of the State
of Delaware and is qualified to do business as a foreign corporation in the
State of California.  As of September 29, 1997, the description of the
capitalization of the Company and its outstanding equity securities contained in
the Company's final Prospectus dated July 11, 1997 is correct in all material
respects, except as set forth on Exhibit C.
                                 --------- 

     3.  Warranties and Covenants of CSC.  CSC hereby represents and warrants
         -------------------------------                                     
to, and covenants with, the Company as of the date hereof as follows:

                3.1  Authorization.  CSC has full power and authority to
                     -------------      
execute, deliver and perform its obligations under this Agreement and the
Warrants. All corporate action on the part of CSC necessary for the
authorization, execution and delivery of this Agreement and the Warrants and the
performance of all obligations of CSC hereunder and thereunder has been taken.
The execution and delivery of this Agreement and the Warrants and the
performance of all obligations of CSC hereunder and thereunder were approved by
CSC's Board of Directors on October 3, 1997. This Agreement and the Warrants are
valid and legally binding obligations of CSC, enforceable against it in
accordance with their terms.

                3.2  No Conflict.  The execution, delivery and performance of
                     -----------       
this Agreement and the Warrants and the consummation of each of the transactions
contemplated hereby and thereby do not and will not (a) conflict with or result
in a breach of the terms, conditions or provisions of, (b) with or without
notice or lapse of time or both, constitute a default under, (c) result in the
creation of any lien, security interest, charge or encumbrance upon CSC's
capital stock or assets pursuant to, (d) with or without notice or lapse of time
or both, give any third party the right to accelerate, cancel or terminate any
obligation under, (e) result in a violation of, or (f) require any order,

                                       3
<PAGE>
 
qualification, waiver, permit, authorization, consent, approval, exemption or
other action by or from, or any registration, notice, declaration, application
or filing to or with, any court or administrative or governmental body or any
other person or entity pursuant to (i) the Certificate of Incorporation or
Bylaws of CSC, (ii) any agreement to which CSC is a party or is bound or to
which its assets are subject or (iii) any law, statute, rule or regulation to
which CSC is subject; provided, however, that with respect to clause (f) of this
                      --------  -------                                         
Section 3.2, no representation or warranty is made as to any such requirements
applicable to CSC as a result of the specific legal or regulatory status of the
Company (including without limitation any agreements between the Company or its
affiliates and any local or municipal government related to the provision of
cable television services within a local area) or as a result of any other facts
that specifically relate to the Company, any business in which the Company has
engaged or proposes to engage or any financing arrangements or transactions
entered into or proposed to be entered into by or on behalf of the Company and
                                                                              
provided, further, that no representation or warranty is made with respect to
- --------  -------                                                            
the application of the HSR Act to the exercise of the Warrants.

                3.3  Accredited Investor Status.  CSC is an "accredited
                     --------------------------    
investor" within the meaning of Regulation D promulgated under the Securities
Act of 1933 (the "SECURITIES ACT").

                3.4  Restricted Securities.  CSC understands that the Warrants
                     ---------------------     
and the Warrant Stock are restricted securities and may not be sold, transferred
or otherwise disposed of without registration under the Securities Act or the
availability of an exemption therefrom, and that in the absence of an effective
registration statement covering such securities or an exemption from
registration, the Warrants and Warrant Stock must be held indefinitely. In the
absence of an effective registration statement under the Securities Act with
respect to the Warrants or any Warrant Stock, CSC shall notify the Company of
any proposed disposition by CSC of the Warrants or Warrant Stock, shall furnish
the Company with a statement of the circumstances surrounding the proposed
disposition and, if reasonably requested by the Company, shall furnish the
Company with an opinion of counsel, reasonably satisfactory to the Company, that
such disposition will not require the registration of such Warrants or such
Warrant Stock under the Securities Act, provided that an opinion of counsel will
not be required for routine sales under Rule 144 under the Securities Act.

     4.   Miscellaneous.
          ------------- 

                4.1  Governing Law.  This Agreement shall be governed by, and
                     -------------                                           
construed in accordance with, in all respects the laws of the State of Delaware,
without regard to the conflicts of law rules of such state.

                4.2  Successors and Assigns.  Except for transfers or
                     ----------------------       
assignments of the Warrants that are not prohibited by this Agreement or the
Warrants, neither this

                                       4
<PAGE>
 
Agreement nor any of the rights, interests or obligations hereunder shall be
assigned by the Company or CSC without the prior written consent of CSC or the
Company, respectively.  Any assignment or delegation in contravention of this
Agreement shall be void and shall not relieve the assigning or delegating party
of any obligation hereunder.  Except as set forth in the preceding sentences,
this Agreement shall inure to the benefit of and be binding upon the parties
hereto and their respective successors and permitted assigns (including without
limitation the restrictions and legend requirements set forth in the Warrants).

                4.3  No Third Party Beneficiaries.  Nothing in this Agreement,
                     ---------------------------- 
whether express or implied, shall be construed to give any person, other than
the parties hereto, any legal or equitable right, remedy or claim under or in
respect of this Agreement.

                4.4  Counterparts.  This Agreement may be executed in any number
                     ------------            
of counterparts with the same effect as if all parties hereto had signed the
same document. Each counterpart shall be enforceable against the parties
actually executing such counterpart, and all counterparts shall be construed
together and shall constitute one instrument.

                4.5  Severability.  If one or more provisions of this Agreement
                     ------------      
are held to be unenforceable under applicable law, such provision shall be
excluded from this Agreement and the balance of the Agreement shall be
interpreted as if such provision were so excluded and shall be enforceable in
accordance with its terms.

                4.6  Interpretation.  In the event of any conflict or
                     --------------   
inconsistency between this Agreement and the Term Sheet, the provisions of this
Agreement shall be controlling.


                4.7  Notices.  Unless otherwise provided, any notice required or
                     -------                                                    
permitted under this Agreement shall be given as follows:


                To CSC:                            To the Company:


                Cablevision Systems Corporation    At Home Corporation
                One Media Crossways                425 Broadway
                Woodbury, NY 11797                 Redwood City, CA 94063
                Attn: Robert P. May                Attn: Kenneth A. Goldman
                      Chief Operating Officer            Chief Financial Officer

                4.8  Public Announcements.  Any press release or other public
                     --------------------                                    
statement issued by any party relating to the first public announcement of this
Agreement or the transactions contemplated hereby shall be mutually agreed to by
the parties.

                                       5
<PAGE>
 
                4.9  Entire Agreement.  This Agreement, the Warrants and the
                     ----------------
Term Sheet constitute the entire agreement between the parties concerning the
subject matter hereof. This Agreement may be amended, modified or waived only by
a written instrument executed by duly authorized representatives of both
parties.

                4.10  Direction Regarding Issuance.  CSC will have the right to
                      ----------------------------      
direct the Company to issue the Warrants to CSC Parent, its wholly owned
subsidiary.

                                       6
<PAGE>
 
          IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.


                              AT HOME CORPORATION


                              By:
                                 --------------------------------
                                 Name:
                                 Title:



                              CABLEVISION SYSTEMS CORPORATION


                              By:
                                 --------------------------------
                                 Name:
                                 Title:

Attachments:
- ----------- 

Exhibit A - Form of Warrant
Exhibit B - Form of Contingent Warrant
Exhibit C - Updates to Representations and Warranties

                                       7
<PAGE>
 
                                   EXHIBIT A
                                FORM OF WARRANT
<PAGE>
 
                                   EXHIBIT B
                           FORM OF CONTINGENT WARRANT






                                       9
<PAGE>
 
                                   EXHIBIT C
                   UPDATES TO REPRESENTATIONS AND WARRANTIES


              CAPITALIZATION OF AT HOME CORPORATION AS OF 9/29/97


        Series of Stock                   Shares Outstanding
        ---------------                   ------------------

        Series A Common                      88,592,701
        Series B Common                      15,400,000
        Series K Common                      14,877,660


Options to purchase 1,729,855 shares of Series A Common have been granted and
are outstanding.

Warrants to purchase 2,300,000 shares of Series A Common have been granted and
are outstanding.

The Company intends to grant a warrant to purchase an additional 100,000 shares
of Series A Common to Intel Corporation.

Secured credit facility with Silicon Valley Bank in an aggregate principal
amount of $8,000,000 (entered into on September 30, 1997).




                                      10

<PAGE>
 
                                                                   EXHIBIT 10.03


     THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES LAWS OF
ANY STATE. THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND
RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT
AND THE APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION
THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE
FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER
OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL, IN FORM AND SUBSTANCE
SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS
IN COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS.

     THE SECURITIES REPRESENTED BY THIS WARRANT ARE SUBJECT TO THAT CERTAIN
STOCKHOLDERS' AGREEMENT, DATED AS OF JULY 16, 1997 AND AS THEREAFTER AMENDED,
AMONG THE COMPANY AND THE OTHER PARTIES THERETO CONTAINING, AMONG OTHER THINGS,
RESTRICTIONS, ON THE SALE, TRANSFER OR OTHER DISPOSITION OF SUCH SECURITIES AND
RESTRICTIONS UPON AND COMMITMENTS TO VOTE ON CERTAIN MATTERS.  A COUNTERPART OF
EACH SUCH AGREEMENT HAS BEEN DEPOSITED WITH THE COMPANY AT ITS PRINCIPAL PLACE
OF BUSINESS, AND THE COMPANY SHALL FURNISH A COPY OF EACH SUCH AGREEMENT TO THE
RECORD HOLDER HEREOF WITHOUT CHARGE UPON WRITTEN REQUEST.

Warrant No.:   W-3
              -----
Issue Date:  October 10, 1997
             ----------------

                   WARRANT TO PURCHASE SERIES A COMMON STOCK

                                       OF

                              AT HOME CORPORATION

     THIS CERTIFIES THAT, in consideration of the sum of one dollar ($1.00)
previously paid in cash and for other good and valuable consideration the
receipt and sufficiency of which is hereby acknowledged, CSC Parent Corporation,
a Delaware corporation (the "Initial Registered Holder") or its permitted
registered assigns (including the Initial Registered Holder, the "Registered
Holder"), is entitled, subject to the terms and conditions of this Warrant, to
purchase from At Home Corporation, a Delaware 
<PAGE>
 
corporation (the "Company"), at any time on or prior to the Expiration Date,
7,875,784 shares of the Company's Series A Common Stock, at an exercise price
equal to fifty cents ($0.50) per share of Series A Common Stock (such price, as
it may be adjusted pursuant to the provisions of Section 5 below, referred to as
the "Exercise Price"), upon surrender of this Warrant at the principal office of
the Company, together with a duly executed subscription form in the form
attached hereto as Exhibit 1 and simultaneous payment of the full exercise price
                   ---------      
for the shares of Warrant Stock so purchased. The Exercise Price and the number
and kind of shares of Warrant Stock purchasable under this Warrant are subject
to adjustment as provided herein.

Notwithstanding anything to the contrary contained in this Warrant, this Warrant
and all rights to purchase Warrant Stock hereunder shall terminate on the
Expiration Date.

     1.   Certain Definitions. The following definitions shall apply for
          -------------------                                           
purposes of this Warrant:

     "Act" means the Securities Act of 1933, as amended.

     "CSC" means Cablevision Systems Corporation, a Delaware corporation.

     "Expiration Date" means 5:00 p.m. Pacific Time on the fifth (5th)
anniversary of the Issue Date.

     "IPO" means the closing of the Company's initial public offering of Series
A Common Stock registered under the Act.

     "Issue Date" means the date of this Warrant.

     "Person" means any individual, corporation, limited liability company,
partnership, joint venture, association, joint stock company, trust,
unincorporated organization, government or agency or political subdivision
thereof, or other entity, whether acting in an individual. fiduciary or other
capacity.

     "Series A Common Stock" means the Company's Series A Common Stock, par
value of $0.01 per share, and stock of any other series or class into which the
same may be changed.

     "SEC" means the Securities and Exchange Commission.

     "Stockholders Agreement" means the Amended and Restated Stockholders'
Agreement, dated as of July 16, 1997, among the Company, TCI Internet Holdings,
Inc., Kleiner Perkins Caufield & Byers VII, KPCB Information Sciences Zaibatsu
Fund II, James Clark, Comcast PC Investments, Inc. and Cox Teleport Providence,
Inc. and certain of their affiliates, as such agreement is amended through the
Issue Date, and as may thereafter be amended from time to time.

     "Warrant" means this Warrant and any warrant(s) delivered in substitution
or exchange therefor, as provided herein.

                                       2
<PAGE>
 
     "Warrant Agreement" means the Warrant Purchase Agreement dated October 10,
1997 among the Company and the Initial Registered Holder relating to the
issuance of this Warrant.

     "Warrant Stock" means shares of Series A Common Stock (or such other class
or series of capital stock of the Company or any successor thereto into which
the Series A Common Stock has been converted), in each case issued upon exercise
of this Warrant.

     2.   Exercise.
          -------- 

          2.1   Exercisability of Warrant. This Warrant is exerciseable in whole
                --------------------------                                      
or in part commencing on the Issue Date and may be exercised at any time on or
before the Expiration Date.

          2.2   Surrender. Subject to compliance with all applicable securities
                ---------                                                      
laws and the provisions of Section 2.1, this Warrant may be exercised in whole
or in part by surrendering this Warrant at the principal office of the Company
at 425 Broadway, Redwood City, California 94063, with the subscription form
attached hereto as Exhibit 1 duly executed by the Registered Holder, accompanied
                   -------                                                      
by payment as set forth in Section 2.3 below.

          2.3   Payment of Exercise Price. Payment shall be made at any time
                -------------------------                                   
with respect to shares of Warrant Stock being purchased hereunder by the payment
to the Company, by cash, check and/or wire transfer, of an amount equal to the
then-applicable Exercise Price per share multiplied by the number of shares of
Warrant Stock then being purchased.

          2.4   Date of Exercise; Fractional Shares. Except as otherwise
                -----------------------------------                     
provided in Section 2.3, this Warrant shall be deemed to have been exercised
immediately prior to the close of business on the date of its surrender for
exercise as provided in Sections 2.2 and 2.3, and the Person entitled to receive
the shares of Warrant Stock issuable upon such exercise shall be treated for all
purposes as the holder of record of such shares as of the close of business on
such date. As soon as practicable on or after such date, the Company shall issue
and deliver to the Person or Persons entitled to receive the same a certificate
or certificates for the number of whole shares of Warrant Stock issuable upon
such exercise, together with cash in lieu of any fraction of a share equal to
such fraction of the current fair market value of one whole share of Warrant
Stock as of the date of exercise, as determined in good faith by the Company's
Board of Directors. No fractional shares may be issued upon any exercise of this
Warrant, and any fractions shall be rounded down to the nearest whole number of
shares.

          2.5   Partial Exercise.  Upon a partial exercise of this Warrant, this
                ----------------                                                
Warrant shall be surrendered by the Registered Holder and replaced with a new
Warrant of like tenor in the name of the Registered Holder providing for the
right to purchase the number of shares of Warrant Stock as to which this Warrant
has not been exercised.

                                       3
<PAGE>
 
          2.6   Taxes. The issuance of certificates for shares of Warrant Stock
                -----                                                          
upon the exercise of this Warrant will be made without charge by the Company to
the Registered Holder for any issue tax (other than applicable income tax).

     3.   Other Representations and Covenants of the Company.
          -------------------------------------------------- 

          3.1   Fully Paid Shares; Reservation. The Company hereby represents
                ------------------------------                               
and warrants to the Registered Holder that all shares of Warrant Stock which may
be issued upon exercise of this Warrant (including all shares of stock of any
other series or class into which the same may be changed) shall have been duly
and validly reserved for issuance and, upon issuance, be duly authorized,
validly issued, fully paid and nonassessable, and free of any liens, claims,
charges, security interests, pledges or encumbrances of any kind, except for
restrictions on transfer and voting restrictions provided for in this Warrant,
the Warrant Agreement, the Stockholders Agreement or under applicable federal
and state securities laws.  The Company shall at all times keep reserved out of
its authorized but unissued shares of Warrant Stock (or shares of stock of any
other series or class into which the same may be changed) such number of
authorized shares of Warrant Stock (or shares of stock of any other series or
class into which the same may be changed) as shall be sufficient to effect the
exercise of this Warrant.  If at any time the number of authorized but unissued
shares of the Company's Warrant Stock (or shares of stock of any other series or
class into which the same may be changed) shall not be sufficient to effect the
exercise of this Warrant, the Company will take such corporate action as may, in
the opinion of its counsel, be necessary to increase its authorized but unissued
shares of Warrant Stock (or shares of stock of any other series or class into
which the same may be changed) to such number of shares of Warrant Stock (or
shares of stock of any other series or class into which the same may be changed)
as shall be sufficient for such purpose.

          3.2   Notices. The Company agrees that it will notify the Registered
                -------                                                       
Holder at least ten (10) business days in advance of the proposed consummation
of any pending consolidation or merger of the Company into any other corporation
or the sale of all or substantially all of the Company's assets to another
corporation, unless after the closing of any such transaction the stockholders
of the Company immediately prior to such transaction would own in excess of
fifty percent (50%) of the voting power of the surviving corporation or its
parent corporation. Such notice shall include a description of all material
terms and conditions of such transaction and the per share value of the
consideration to be paid in connection therewith, and other information given by
the Company to the holders of its Series A Common Stock in connection with their
approval thereof.

          3.3   No Impairment. The Company will not, by amendment of its
                -------------                                           
Certificate of Incorporation or Bylaws, or through reorganization,
consolidation, merger, dissolution, issue or sale of securities, sale of assets
or any other voluntary action, willfully avoid or seek to avoid the observance
or performance of any of the terms of this Warrant, but will at all times in
good faith assist in the carrying out of all such terms and in the taking of all
such action as may be necessary or appropriate in order to protect the

                                       4
<PAGE>
 
rights of the Registered Holder under this Warrant against wrongful impairment.
Without limiting the generality of the foregoing, the Company: (i) will not set
nor increase the par value of any shares of stock issuable upon exercise of this
Warrant above the amount payable therefor upon such exercise, and (ii) will take
all such action as may be necessary or appropriate in order that the Company may
validly and legally issue fully paid and non-assessable shares of Warrant Stock
upon the exercise of this Warrant.

     4.   Transfer Restrictions.
          --------------------- 

          4.1   Mechanics and Effects of Transfer.  This Warrant is subject to
                ---------------------------------                             
the restrictions on sale, transfer and other dispositions set forth in Article 4
of the Stockholders Agreement.  Any assignment, conveyance or transfer of the
Warrant or the rights hereunder shall be made on the books of the Company
maintained for such purpose at the principal office of the Company upon
surrender of this Warrant and a properly completed assignment in the form of
Exhibit 2 hereto. All transferees under this Section 4 will be bound by the
- ---------                                                                  
provisions of this Section 4. Notwithstanding the foregoing, this Warrant and
the rights hereunder may not be assigned, conveyed or transferred unless such
assignment, conveyance or transfer also complies with all applicable securities
laws, the provisions of the Warrant Agreement and the provisions of Section 8.2
hereof.

          4.2   Market Stand-Off Agreement. The Registered Holder hereby agrees
                --------------------------                                     
that it shall not, to the extent specified by the Company and the applicable
managing underwriters of Series A Common Stock (or other securities) of the
Company offered and sold in the IPO, sell, offer to sell, contract to sell
(including without limitation any short sale), grant any option to purchase or
otherwise transfer or dispose of any equity securities of the Company (other
than the purchase and exercise of this Warrant) during the period of 180 days
following the effective date of the IPO.

          4.3   Legends; Notations. The certificates evidencing the Warrant
                ------------------
Stock shall be endorsed with the legends set forth below:

                (a)  a conspicuously noted legend in substantially the following
          form:

     "THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES LAWS OF
ANY STATE. THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND
RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT
AND THE APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION
THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE
FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER
OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL IN FORM AND SUBSTANCE
SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS
IN

                                       5
<PAGE>
 
COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS."

               (b)  any legend required by any applicable state securities law;
          and

               (c)  a conspicuously noted legend in substantially the following
          form:

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO COVENANTS IN
THAT CERTAIN WARRANT DATED AS OF OCTOBER 10, 1997 AND A WARRANT PURCHASE
AGREEMENT DATED OCTOBER 10, 1997 BETWEEN THE COMPANY AND THE REGISTERED HOLDER
THEREOF CONTAINING, AMONG OTHER THINGS, RESTRICTIONS ON THE SALE, TRANSFER OR
OTHER DISPOSITIONS OF SUCH SECURITIES. A COUNTERPART OF SUCH AGREEMENT HAS BEEN
DEPOSITED WITH THE COMPANY AT ITS PRINCIPAL PLACE OF BUSINESS, AND THE COMPANY
SHALL FURNISH A COPY OF EACH SUCH AGREEMENT TO THE RECORD HOLDER HEREOF WITHOUT
CHARGE UPON WRITTEN REQUEST."; and

               (d) any other legend required by the Stockholders Agreement.

          The Company shall make a notation on its stock books regarding the
restrictions on transfer of the Warrants and Warrant Stock required by
applicable securities and other laws, this Warrant and the Warrant Agreement,
and will transfer securities on the books of the Company only to the extent not
inconsistent therewith. Without limiting the foregoing, the Company shall refuse
to register any transfer of the Warrants or Warrant Stock not made in accordance
with the registration requirements of the Act or pursuant to an applicable
exemption from registration under the Act.

     5.   Adjustment of Exercise Price; Number and Kind of Shares. The number
          -------------------------------------------------------            
and kind of shares of Warrant Stock issuable upon exercise of this Warrant (or
any shares of stock or other securities or property at the time receivable or
issuable upon exercise of this Warrant) and the Exercise Price therefor, are
subject to adjustment upon the occurrence of the following events:

          5.1.  Adjustment for Stock Splits, Stock Subdivisions or Combinations
                ---------------------------------------------------------------
of Shares. The Exercise Price of this Warrant shall be proportionally decreased
- ---------                                                                      
and the number of shares of Series A Common Stock issuable upon exercise of this
Warrant (or any shares of stock or other securities at the time issuable upon
exercise of this Warrant), shall be proportionally increased to reflect any
stock split or subdivision of the Company's Series A Common Stock (or any shares
of stock or other securities at the time issuable upon exercise of this
Warrant). The Exercise Price of this Warrant shall be proportionally increased
and the number of shares of Series A Common Stock issuable upon exercise of this
Warrant (or any shares of stock or other securities at the time issuable upon
exercise of this Warrant) shall be proportionally decreased to reflect any
combination of the Company's Series A Common Stock (or any shares of stock or
other

                                       6
<PAGE>
 
securities at the time issuable upon exercise of this Warrant) into a smaller
number of shares.

          5.2   Adjustment for Reorganization, Consolidation, Merger. In case of
                ----------------------------------------------------            
any reorganization of the Company (or of any other corporation, the stock or
other securities of which are at the time receivable on the exercise of this
Warrant), after the Issue Date, or in case, after such date, the Company (or any
such corporation) shall consolidate with or merge into another corporation or
convey all or substantially all of its assets to another corporation or other
entity, then, and in each such case, the Registered Holder of this Warrant, upon
any permitted exercise of this Warrant (as provided in Section 2), at any time
after the consummation of such reorganization, consolidation, merger, or
conveyance, shall be entitled to receive, in lieu of the stock or other
securities and property receivable upon the exercise of this Warrant prior to
such consummation, the stock or other securities or property to which such
Registered Holder would have been entitled upon the consummation of such
reorganization, consolidation, merger or conveyance if such Registered Holder
had exercised this Warrant immediately prior thereto, all subject to further
adjustment as provided in this Section 5, and the successor or purchasing
corporation or other entity in such reorganization, consolidation, merger or
conveyance (if other than the Company) shall duly execute and deliver to the
Registered Holder a supplement hereto acknowledging such corporation's or
entity's obligations under this Warrant; and in each such case, the terms of
this Warrant (including, the exercisability, transfer and adjustment provisions
of this Warrant) shall be applicable to the shares of stock or other securities
or property receivable upon the exercise of this Warrant after the consummation
of such reorganization, consolidation, merger or conveyance. The foregoing
provisions of this Section 5.2 shall similarly apply to successive
reorganizations, consolidations, mergers, sales and transfers and to the stock
or securities of any other corporation that are at the time receivable upon the
exercise of this Warrant. If the per-share consideration payable to the
Registered Holder hereof for shares in connection with any such transaction is
in a form other than cash or marketable securities, then the value of such
consideration shall be determined in good faith by the Company's Board of
Directors. In all events, appropriate adjustment (as determined in good faith by
the Company's Board of Directors) shall be made in the application of the
provisions of this Warrant with respect to the rights and interests of the
Registered Holder after the transaction, to the end that the provisions of this
Warrant shall be applicable after that event, as near as reasonably may be, in
relation to any shares or other property deliverable after that event upon
exercise of this Warrant.

          5.3.   Adjustment for Dividends or Distributions of Stock or Other
                 -----------------------------------------------------------
Securities or Property. In case the Company shall make or issue, or shall fix a
- ----------------------                                                         
record date for the determination of eligible Registered Holders entitled to
receive, a dividend or other distribution with respect to the Series A Common
Stock (or any shares of stock or other securities at the time issuable upon
exercise of the Warrant) payable in (a) securities of the Company or (b) assets
(excluding cash dividends paid or payable solely out of retained earnings),
then, in each such case, the Registered Holder of this Warrant on exercise
hereof at any time after the record date of such dividend or other distribution,
shall receive, in addition to the shares of Series A Common Stock (or such other
stock or

                                       7
<PAGE>
 
securities) issuable on such exercise prior to such date, and without the
payment of additional consideration therefor, the securities or such other
assets of the Company to which such Registered Holder would have been entitled
upon such date if such Registered Holder had exercised this Warrant on the date
hereof and had thereafter, during the period from the date hereof to and
including the date of such exercise, retained such shares and/or all other
additional stock available by it as aforesaid during such period giving effect
to all adjustments called for by this Section 5 (and the Company shall place
such securities or other assets into escrow until receipt by the Registered
Holder); provided, that if any such dividend or distribution consists of the
         --------                                                           
securities of another entity controlled by the Company, the Company shall make
provision reasonably acceptable to the Registered Holder to provide the
Registered Holder with substantially the same economic benefits as if the
Registered Holder had exercised this Warrant immediately prior to such record
date and had received such securities in such dividend or distribution.

          5.4.   Reclassification. If the Company, by reclassification of
                 ----------------                                        
securities or otherwise, shall change any of the securities as to which purchase
rights under this Warrant exist into the same or a different number of
securities of any other class or classes, this Warrant shall thereafter
represent the right to acquire such number and kind of securities as would have
been issuable as the result of such change with respect to the securities that
were subject to the purchase rights under this Warrant immediately prior to such
reclassification or other change and the Exercise Price therefore shall be
appropriately adjusted, all subject to further adjustment as provided in this
Section 5.

     6.   Certificate as to Adjustments. In each case of any adjustment in
          -----------------------------                                   
either the Exercise Price or in the number of shares of Warrant Stock, or other
securities or property receivable upon the exercise of this Warrant, the Chief
Financial Officer of the Company shall promptly thereafter compute such
adjustment in accordance with the terms of this Warrant and prepare a
certificate setting forth such adjustment and showing in detail the facts upon
which such adjustment is based, including a statement of the adjusted Exercise
Price. The Company will cause copies of such certificate to be mailed (by first
class mail, postage prepaid) to the Registered Holder.

     7.   Loss or Mutilation. Upon receipt by the Company of evidence reasonably
          ------------------                                                    
satisfactory to it of the ownership, and the loss, theft, destruction or
mutilation, of this Warrant, and of indemnity reasonably satisfactory to it, and
(in the case of mutilation) upon surrender and cancellation of this Warrant, the
Company will execute and deliver in lieu thereof a new Warrant of like tenor.

     8.   Representations and Warranties of the Registered Holder.
          ------------------------------------------------------- 

          8.1   Restrictions under Securities Laws. The Registered Holder
                ----------------------------------                       
understands that neither the offer and sale of this Warrant nor the offer and
sale of shares of Warrant Stock that may be purchased upon exercise thereof have
been registered under the Act, or any state securities laws. As a condition to
the issuance of this Warrant and to its exercise the Registered Holder hereby
represents and warrants to the Company that:

                                       8
<PAGE>
 
          (a)  The Registered Holder is capable of evaluating the merits and
risks of any investment in the Warrant and the underlying shares of Warrant
Stock (collectively, the "Securities"), is financially capable of bearing a
total loss of this investment and either: (i) has a preexisting personal or
business relationship with the Company or its principals; (ii) by reason of the
Registered Holder's business or financial experience, has the capacity to
protect his or its own interests in connection with this investment; or (iii) if
the Registered Holder is the Initial Registered Holder, is an "accredited
investor" within the meaning of Regulation D promulgated under the Act, as
amended.

          (b)  The Registered Holder has had access to all information regarding
the Company, its present and prospective business, assets, liabilities and
financial condition that the Registered Holder considers important to making the
decision to acquire the Securities and has had ample opportunity to ask
questions of and receive answers from the Company's representatives concerning
an investment in the Securities and to obtain any and all documents requested in
order to supplement or verify any of the information supplied.

          (c)  The Registered Holder understands that the Securities shall be
deemed restricted securities under the Act and may not be resold unless they are
registered under the Act and any applicable State securities law, or in the
opinion of counsel in form and substance satisfactory to the Company, an
exemption from such registration is available.

          (d)  The Registered Holder is aware of Rule 144 promulgated under the
Act, which rule, as in effect on the date hereof, provides, in substance, that:
(i) after one year from the date restricted securities have been purchased and
fully paid for, a holder may transfer restricted securities provided certain
conditions are met (e.g., certain public information is available about the
Company), and specific limitations on the amount of shares which can be sold
within certain periods and the manner in which such shares must be sold are
complied with; and (ii) after two years from the date the securities have been
purchased and fully paid for, holders who are not "affiliates" of the Company
may sell restricted securities without satisfying such conditions.

          (e)  The Registered Holder further understands that if the
requirements of Rule 144 are not met, registration under the Act or compliance
with some other registration exemption will be required for any disposition of
the Securities; and that, although Rule 144 is not exclusive, the SEC has
expressed its opinion that persons proposing to sell restricted securities other
than in a registered offering or other than pursuant to Rule 144 will have a
substantial burden of proof in establishing that an exemption from registration
is available for such offers or sales and such persons and the brokers who
participate in the transactions do so at their own risk.

     8.2   Compliance with U.S. Securities Laws. The Registered Holder, by
           ------------------------------------                           
acceptance hereof, agrees that, absent an effective registration statement filed
with the SEC under the Act, covering the disposition or sale of the Securities
or other securities of

                                       9
<PAGE>
 
the Company issued or issuable upon exercise hereof, as the case may be, and
registration or qualification under applicable state securities laws, such
Registered Holder will not sell, transfer, pledge, or hypothecate any or all
such Securities or other securities, as the case may be, unless either (i) the
Company has received an opinion of counsel, in form and substance reasonably
satisfactory to the Company, to the effect that such registration is not
required in connection with such disposition or (ii) the sale of such Securities
and/or securities is made pursuant to SEC Rule 144.

     9.   No Rights or Liabilities as Stockholder. This Warrant does not by
          ---------------------------------------                          
itself entitle the Registered Holder to any voting rights or other rights as a
stockholder of the Company. In the absence of affirmative action by the
Registered Holder to purchase Warrant Stock by exercise of this Warrant, no
provisions of this Warrant, and no enumeration herein of the rights or
privileges of the Registered Holder, shall cause such Registered Holder to be a
stockholder of the Company for any purpose.

     10.   Regulatory Compliance. The Company and the Registered Holder hereby
           ---------------------                                              
acknowledge that exercise of this Warrant by the Registered Holder is subject to
receipt of all necessary governmental consents and approvals and may subject the
Company and/or the Registered Holder to the filing requirements of the Hart-
Scott-Rodino Antitrust Improvements Act of 1976, as amended (the "HSR Act"), and
that the Registered Holder may be prevented from exercising this Warrant until
receipt of all necessary governmental consents and approvals and the expiration
or early termination of all waiting periods imposed by the HSR Act.  Promptly
following the Registered Holder's notice of exercise or other written request
from the Registered Holder, the Company and the Registered Holder will use their
respective commercially reasonable efforts to make all filings necessary to
obtain such consents and approvals and/or to cause the expiration or termination
of any applicable waiting period under the HSR Act.  In the event that the
Registered Holder has been unable to exercise this Warrant prior to the
Expiration Date because of the failure to receive a governmental consent or
approval or the failure of the waiting period under the HSR Act to have expired
or have terminated (despite the Registered Holder's and the Company's continuing
use of commercially reasonable efforts to obtain such consent or approval or the
expiration or termination of such waiting period), then CSC or the Initial
Registered Holder, as the case may be, shall have the right to acquire upon
exercise on the Expiration Date of the then-remaining unexercised portion of
this Warrant shares of a series or class of non-voting, transferable, equity
securities of the Company that are convertible at any time into the number of
shares of Warrant Stock that CSC or the Initial Registered Holder would have
obtained upon exercise of this Warrant immediately prior thereto and upon
payment of the aggregate Exercise Price that would have been so payable; and the
Company will take such steps as may be necessary to effect the creation,
authorization and issuance of such securities.  The terms of such securities
will be designed to provide the same economic benefits as the Warrant Stock.

     11.  Severability. If any term, provision, covenant or restriction of this
          ------------                                                         
Warrant is held by a court of competent jurisdiction to be invalid, void or
unenforceable, the

                                       10
<PAGE>
 
remainder of the terms, provisions, covenants and restrictions of this Warrant
shall remain in full force and effect and shall in no way be affected, impaired
or invalidated.

     12.  No Inconsistent Agreements. The Company will not on or after the date
          --------------------------                                           
of this Warrant enter into any agreement with respect to its securities which is
inconsistent with the rights granted to the Registered Holder of this Warrant or
otherwise conflicts with the provisions hereof. The rights granted to the
Registered Holder hereunder do not in any way conflict with and are not
inconsistent with the rights granted to a registered holder of the Company's
securities under any other agreements, except rights that have been waived.

     13.  Headings. The headings in this Warrant are for purposes of
          --------                                                  
convenience in reference only, and shall not be deemed to constitute a part
hereof.

     14.  Law Governing. This Warrant shall be construed and enforced in
          -------------                                                 
accordance with, and governed by, the internal laws of the State of Delaware,
excluding that body of law applicable to conflicts of laws.

     15.  Terms Binding. By acceptance of this Warrant, the Registered Holder of
          -------------                                                         
this Warrant (and each subsequent assignee, transferee or Registered Holder of
this Warrant) accepts and agrees to be bound by all the terms and conditions of
this Warrant.

     16.  Counterparts. This Warrant may be executed in one or more
          ------------                                             
counterparts, each of which shall be an original and all of which together shall
constitute one and the same instrument.

                                       11
<PAGE>
 
IN WITNESS WHEREOF, the Company and the Registered Holder have executed this
Warrant as of the Issue Date.

THE COMPANY:                        ACKNOWLEDGED AND ACCEPTED
                                    BY REGISTERED HOLDER:

AT HOME CORPORATION                 CSC PARENT
                                    CORPORATION


By:                                 By:
    --------------------------         ----------------------------

Name:                               Name:
     -------------------------           --------------------------

Title:                              Title:
      ------------------------            -------------------------

                           [WARRANT SIGNATURE PAGE]

                                       12
<PAGE>
 
                                                                       Exhibit 1
                                                                       ---------
                              FORM OF SUBSCRIPTION
                              --------------------

                  (To be signed only upon exercise of Warrant)

To:  At Home Corporation
     425 Broadway
     Redwood City, California 94063
     Attention: President

cc:  Fenwick & West LLP
     Two Palo Alto Square
     Palo Alto, CA 94306
     Attention: Gordon K. Davidson, Esq.

     (1) The undersigned hereby elects to purchase _______ shares of Series A
Common Stock of At Home Corporation, a Delaware corporation (the "Company") (or
such other class or series of capital stock of the Company or any successor
thereto into which the Series A Common Stock has been converted (describe:
_____________)) or other securities of the Company issuable pursuant to Section
10 of the attached Warrant (describe: _____________) (collectively, "Applicable
Securities"), all pursuant to the terms of the attached Warrant, and tenders
herewith payment of the purchase price for such shares in full.

     (2)  In exercising this Warrant, the undersigned hereby confirms and
acknowledges that the representations and warranties of the Undersigned set
forth in Section 8 of the Warrant are true and correct as of this date.

     (3)  Please issue a certificate or certificates representing said shares of
Applicable Securities in the name specified below:


                              ----------------------------------
                              (Name)

                              ----------------------------------
                              (Address)

                              ----------------------------------
                              (City, State, Zip Code)

     (4)  Please issue a new Warrant for the unexercised portion of the attached
Warrant in the name of the undersigned or in such other name as is specified
below:

                                       13
<PAGE>
 
- ------------------------- 
(Other Name)

                              REGISTERED HOLDER



                              ------------------------------------
                              (Name of Registered Holder)


                              ------------------------------------
                              (Signature of Registered Holder)


                              ------------------------------------
                              (Title)


                              ------------------------------------
                              (Date)

                                       14
<PAGE>
 
                                                                       Exhibit 2
                                                                       ---------
                               FORM OF ASSIGNMENT
                               ------------------
                                        
     FOR VALUE RECEIVED, the undersigned Registered Holder of the attached
Warrant hereby sells, assigns and transfers unto each of the Assignee(s) named
below all of the rights of the undersigned under such Warrant, with respect to
that number, class and series of shares of Warrant Stock set forth below:

                                              Number, Class and
                                              Series of Shares of
Name of Assignee       Address                Warrant Stock Affected
- ----------------       -------                ----------------------



and does hereby irrevocably constitute and appoint the Secretary of At Home
Corporation, a Delaware corporation (the "Company") as attorney to make such
transfer on the books of the Company maintained for such purpose, with full
power of substitution in the premises.

Dated:

                              REGISTERED HOLDER

                              Name of Registered Holder:


 
                              -------------------------------------

                              By:
                                    -------------------------------

                              Name:
                                    -------------------------------

                              Title:
                                    -------------------------------

                                       15

<PAGE>
 
                                                                   EXHIBIT 10.04


THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES
ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES LAWS OF ANY STATE.
THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND
MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT AND THE
APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION
THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE
FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER
OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL, IN FORM AND SUBSTANCE
SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS
IN COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS.

     THE SECURITIES REPRESENTED BY THIS WARRANT ARE SUBJECT TO THAT CERTAIN
STOCKHOLDERS' AGREEMENT, DATED AS OF JULY 16, 1997 AND AS THEREAFTER AMENDED,
AMONG THE COMPANY AND THE OTHER PARTIES THERETO CONTAINING, AMONG OTHER THINGS,
RESTRICTIONS, ON THE SALE, TRANSFER OR OTHER DISPOSITION OF SUCH SECURITIES AND
RESTRICTIONS UPON AND COMMITMENTS TO VOTE ON CERTAIN MATTERS.  A COUNTERPART OF
EACH SUCH AGREEMENT HAS BEEN DEPOSITED WITH THE COMPANY AT ITS PRINCIPAL PLACE
OF BUSINESS, AND THE COMPANY SHALL FURNISH A COPY OF EACH SUCH AGREEMENT TO THE
RECORD HOLDER HEREOF WITHOUT CHARGE UPON WRITTEN REQUEST.

Warrant No.:   W-4
              -----
Issue Date:  October 10, 1997
             ----------------

              CONTINGENT WARRANT TO PURCHASE SERIES A COMMON STOCK

                                       OF

                              AT HOME CORPORATION

     THIS CERTIFIES THAT, in consideration of the sum of one dollar ($1.00)
previously paid in cash and for other good and valuable consideration the
receipt and sufficiency of which is hereby acknowledged, CSC Parent Corporation,
a Delaware corporation (the "Initial Registered Holder") or its permitted
                             -------------------------
registered assigns (including the Initial Registered Holder, the "Registered
                                                                  ----------
Holder"), is entitled, subject to the terms and conditions of this Warrant, to
- ------
purchase from At Home Corporation, a Delaware 
<PAGE>
 
corporation (the "Company"), from time to time on or prior to the Expiration
Date, the Applicable Number (as hereinafter defined) of shares of the Company's
Series A Common Stock, at an exercise price equal to fifty cents ($0.50) per
share of Series A Common Stock (such price, as it may be adjusted pursuant to
the provisions of Section 5 below, referred to as the "Exercise Price"), upon
surrender of this Warrant at the principal office of the Company, together with
a duly executed subscription form in the form attached hereto as Exhibit 1 and
                                                                 ---------    
simultaneous payment of the full exercise price for the shares of Warrant Stock
so purchased.  The Exercise Price and the number and kind of shares of Warrant
Stock purchasable under this Warrant are subject to adjustment as provided
herein.

Notwithstanding anything to the contrary contained in this Warrant, this Warrant
and all rights to purchase Warrant Stock hereunder shall terminate on the
Expiration Date.

     1.   Certain Definitions. The following definitions shall apply for
          -------------------                                           
purposes of this Warrant:

     "Act" means the Securities Act of 1933, as amended.

     "Applicable Number" means 3,071,152 shares of the Company's Series A Common
Stock (subject to adjustment as provided in this Warrant), which amount is
subject to reduction from time to time prior to the Expiration Date by (x) an
amount equal to the number of shares of Series A Common Stock equal to the
product of (i) the number of Homes Passed as of September 30, 1997 by
Contributed Systems in respect of which any agreement (including the
Contribution Agreement) providing for the transfer of such Contributed Systems
to CSC, the Initial Registered Holder or their Controlled Affiliates has been
terminated (other than by consummation thereof) and (ii) two (subject to
appropriate adjustments to give effect to any stock splits, reverse stock
splits, stock dividends, recapitalizations and the like occurring after
September 29, 1997), and (y) upon the consummation of an Exchange, an amount
equal to the product of (i) the number of Homes Passed as of September 30, 1997
by the Exchanged System that is the subject of such Exchange and (ii) two
(subject to appropriate adjustments to give effect to any stock splits, reverse
stock splits, stock dividends, recapitalizations and the like occurring after
September 29, 1997).

     "Contributed Systems" has the meaning given to such term in the Term Sheet.

     "Contribution Agreement" has the meaning given to such term in the Term
Sheet.

     "Controlled Affiliate" has the meaning given to such term in the
Stockholders Agreement.

     "CSC" means Cablevision Systems Corporation, a Delaware corporation.

     "Exchange" has the meaning given to such term in the Term Sheet.

     "Exchanged System" has the meaning given to such term in the Term Sheet.

                                       2
<PAGE>
 
     "Expiration Date" means 5:00 p.m. Pacific Time on the earlier to occur of
(i) the fifth (5th) anniversary of the Issue Date and (ii) the date, if any,
that the Applicable Number is reduced to zero.

     "Homes Passed" means the number of residential homes that can be connected
to a cable distribution system; provided that each residential unit in a
                                --------                                
multiple dwelling unit shall be counted as one Home Passed.  When used in the
calculation of the Applicable Number, "Homes Passed" shall refer to the number
of Homes Passed by the relevant Contributed System as set forth in the
certification letter of TCI, dated October 9, 1997.

     "IPO" means the closing of the Company's initial public offering of Series
A Common Stock registered under the Act.

     "Issue Date" means the date of this Warrant.

     "Person" means any individual, corporation, limited liability company,
partnership, joint venture, association, joint stock company, trust,
unincorporated organization, government or agency or political subdivision
thereof, or other entity, whether acting in an individual. fiduciary or other
capacity.

     "Series A Common Stock" means the Company's Series A Common Stock, par
value of $0.01 per share, and stock of any other series or class into which the
same may be changed.

     "SEC" means the Securities and Exchange Commission.

     "Stockholders Agreement" means the Amended and Restated Stockholders'
Agreement, dated as of July 16, 1997, among the Company, TCI Internet Holdings,
Inc., Kleiner Perkins Caufield & Byers VII, KPCB Information Sciences Zaibatsu
Fund II, James Clark, Comcast PC Investments, Inc. and Cox Teleport Providence,
Inc. and certain of their affiliates, as such agreement is amended through the
Issue Date, and as may thereafter be amended from time to time.

     "TCI" has the meaning given to such term in the Term Sheet.

     "Term Sheet" has the meaning given to such term in the Warrant Agreement.

     "Warrant" means this Warrant and any warrant(s) delivered in substitution
or exchange therefor, as provided herein.

     "Warrant Agreement" means the Warrant Purchase Agreement dated October 10,
1997 among the Company and the Initial Registered Holder relating to the
issuance of this Warrant.

     "Warrant Stock" means shares of Series A Common Stock (or such other class
or series of capital stock of the Company or any successor thereto into which
the Series A Common Stock has been converted), in each case issued upon exercise
of this Warrant.

                                       3
<PAGE>
 
     2.   Exercise.
          -------- 

          2.1   Exercisability of Warrant.  This Warrant is not immediately
                --------------------------                                 
exercisable, and will become exercisable on and after the Issue Date from time
to time with respect to that number of shares of Series A Common Stock equal to
the product of (i) the number of Homes Passed by the Contributed Systems, as and
to the extent that any of such Contributed Systems are transferred to CSC, the
Initial Registered Holder or any of their Controlled Affiliates, and (ii) two
(subject to appropriate adjustments to give effect to any stock splits, reverse
stock splits, stock dividends, recapitalizations and the like occurring after
September 29, 1997).  In no event will this Warrant become exercisable for more
than the Applicable Number of shares of Series A Common Stock (subject to
adjustment as provided in this Warrant).  Upon any exercise of this Warrant (or
as reasonably requested by the Company from time to time), the Registered Holder
shall certify in writing to the Company (x) the identity of Contributed Systems
(i) transferred to CSC, the Initial Registered Holder or any of their Controlled
Affiliates and/or (ii) in respect of which any agreement (including the
Contribution Agreement) providing for the transfer of such Contributed Systems
to CSC, the Initial Registered Holder or their Controlled Affiliates has been
terminated (other than by consummation thereof) and (y) the identity of
Exchanged Systems as to which Exchanges have been consummated.

          2.2   Surrender. Subject to compliance with all applicable securities
                ---------                                                      
laws and the provisions of Section 2.1, this Warrant may be exercised in whole
or in part by surrendering this Warrant at the principal office of the Company
at 425 Broadway, Redwood City, California 94063, with the subscription form
attached hereto as Exhibit 1 duly executed by the Registered Holder, accompanied
                   -------                                                      
by payment as set forth in Section 2.3 below.

          2.3   Payment of Exercise Price. Payment shall be made at any time
                -------------------------                                   
with respect to shares of Warrant Stock being purchased hereunder by the payment
to the Company, by cash, check and/or wire transfer, of an amount equal to the
then-applicable Exercise Price per share multiplied by the number of shares of
Warrant Stock then being purchased.

          2.4   Date of Exercise; Fractional Shares. Except as otherwise
                -----------------------------------                     
provided in Section 2.3, this Warrant shall be deemed to have been exercised
immediately prior to the close of business on the date of its surrender for
exercise as provided in Sections 2.2 and 2.3, and the Person entitled to receive
the shares of Warrant Stock issuable upon such exercise shall be treated for all
purposes as the holder of record of such shares as of the close of business on
such date. As soon as practicable on or after such date, the Company shall issue
and deliver to the Person or Persons entitled to receive the same a certificate
or certificates for the number of whole shares of Warrant Stock issuable upon
such exercise, together with cash in lieu of any fraction of a share equal to
such fraction of the current fair market value of one whole share of Warrant
Stock as of the date of exercise, as determined in good faith by the Company's
Board of Directors. No fractional shares may

                                       4
<PAGE>
 
be issued upon any exercise of this Warrant, and any fractions shall be rounded
down to the nearest whole number of shares.

          2.5   Partial Exercise.  Upon a partial exercise of this Warrant, this
                ----------------                                                
Warrant shall be surrendered by the Registered Holder and replaced with a new
Warrant of like tenor in the name of the Registered Holder providing for the
right to purchase the number of shares of Warrant Stock as to which this Warrant
has not been exercised.

          2.6   Taxes. The issuance of certificates for shares of Warrant Stock
                -----                                                          
upon the exercise of this Warrant will be made without charge by the Company to
the Registered Holder for any issue tax (other than applicable income tax).

     3.   Other Representations and Covenants of the Company.
          -------------------------------------------------- 

          3.1   Fully Paid Shares; Reservation. The Company hereby represents
                ------------------------------                               
and warrants to the Registered Holder that all shares of Warrant Stock which may
be issued upon exercise of this Warrant (including all shares of stock of any
other series or class into which the same may be changed) shall have been duly
and validly reserved for issuance and, upon issuance, be duly authorized,
validly issued, fully paid and nonassessable, and free of any liens, claims,
charges, security interests, pledges or encumbrances of any kind, except for
restrictions on transfer and voting restrictions provided for in this Warrant,
the Warrant Agreement, the Stockholders Agreement or under applicable federal
and state securities laws.  The Company shall at all times keep reserved out of
its authorized but unissued shares of Warrant Stock (or shares of stock of any
other series or class into which the same may be changed) such number of
authorized shares of Warrant Stock (or shares of stock of any other series or
class into which the same may be changed) as shall be sufficient to effect the
exercise of this Warrant.  If at any time the number of authorized but unissued
shares of the Company's Warrant Stock (or shares of stock of any other series or
class into which the same may be changed) shall not be sufficient to effect the
exercise of this Warrant, the Company will take such corporate action as may, in
the opinion of its counsel, be necessary to increase its authorized but unissued
shares of Warrant Stock (or shares of stock of any other series or class into
which the same may be changed) to such number of shares of Warrant Stock (or
shares of stock of any other series or class into which the same may be changed)
as shall be sufficient for such purpose.

          3.2   Notices. The Company agrees that it will notify the Registered
                -------                                                       
Holder at least ten (10) business days in advance of the proposed consummation
of any pending consolidation or merger of the Company into any other corporation
or the sale of all or substantially all of the Company's assets to another
corporation, unless after the closing of any such transaction the stockholders
of the Company immediately prior to such transaction would own in excess of
fifty percent (50%) of the voting power of the surviving corporation or its
parent corporation. Such notice shall include a description of all material
terms and conditions of such transaction and the per share value of the
consideration to be paid in connection therewith, and other information given by
the

                                       5
<PAGE>
 
Company to the holders of its Series A Common Stock in connection with their
approval thereof.

          3.3   No Impairment. The Company will not, by amendment of its
                -------------                                           
Certificate of Incorporation or Bylaws, or through reorganization,
consolidation, merger, dissolution, issue or sale of securities, sale of assets
or any other voluntary action, willfully avoid or seek to avoid the observance
or performance of any of the terms of this Warrant, but will at all times in
good faith assist in the carrying out of all such terms and in the taking of all
such action as may be necessary or appropriate in order to protect the rights of
the Registered Holder under this Warrant against wrongful impairment. Without
limiting the generality of the foregoing, the Company: (i) will not set nor
increase the par value of any shares of stock issuable upon exercise of this
Warrant above the amount payable therefor upon such exercise, and (ii) will take
all such action as may be necessary or appropriate in order that the Company may
validly and legally issue fully paid and non-assessable shares of Warrant Stock
upon the exercise of this Warrant.

    4.   Transfer Restrictions.
         --------------------- 

         4.1   Mechanics and Effects of Transfer.  This Warrant is subject to
               ---------------------------------                             
the restrictions on sale, transfer and other dispositions set forth in Article 4
of the Stockholders Agreement.  Any assignment, conveyance or transfer of the
Warrant or the rights hereunder shall be made on the books of the Company
maintained for such purpose at the principal office of the Company upon
surrender of this Warrant and a properly completed assignment in the form of
                                                                            
Exhibit 2 hereto. All transferees under this Section 4 will be bound by the
- ---------                                                                  
provisions of this Section 4. Notwithstanding the foregoing, this Warrant and
the rights hereunder may not be assigned, conveyed or transferred unless such
assignment, conveyance or transfer also complies with all applicable securities
laws, the provisions of the Warrant Agreement and the provisions of Section 8.2
hereof.

         4.2   Market Stand-Off Agreement. The Registered Holder hereby agrees
               --------------------------                                     
that it shall not, to the extent specified by the Company and the applicable
managing underwriters of Series A Common Stock (or other securities) of the
Company offered and sold in the IPO, sell, offer to sell, contract to sell
(including without limitation any short sale), grant any option to purchase or
otherwise transfer or dispose of any equity securities of the Company (other
than the purchase and exercise of this Warrant) during the period of 180 days
following the effective date of the IPO.

         4.3   Legends; Notations. The certificates evidencing the Warrant Stock
               ------------------                                               
shall be endorsed with the legends set forth below:

               (a)  a conspicuously noted legend in substantially the following
          form:

     "THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES LAWS OF
ANY STATE. THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND

                                       6
<PAGE>
 
RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT
AND THE APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION
THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE
FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER
OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL IN FORM AND SUBSTANCE
SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS
IN COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS."

               (b)  any legend required by any applicable state securities law;
          and

               (c)  a conspicuously noted legend in substantially the following
          form:

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO COVENANTS IN
THAT CERTAIN WARRANT DATED AS OF OCTOBER 10, 1997 AND A WARRANT PURCHASE
AGREEMENT DATED OCTOBER 10, 1997 BETWEEN THE COMPANY AND THE REGISTERED HOLDER
THEREOF CONTAINING, AMONG OTHER THINGS, RESTRICTIONS ON THE SALE, TRANSFER OR
OTHER DISPOSITIONS OF SUCH SECURITIES. A COUNTERPART OF SUCH AGREEMENT HAS BEEN
DEPOSITED WITH THE COMPANY AT ITS PRINCIPAL PLACE OF BUSINESS, AND THE COMPANY
SHALL FURNISH A COPY OF EACH SUCH AGREEMENT TO THE RECORD HOLDER HEREOF WITHOUT
CHARGE UPON WRITTEN REQUEST."; and

               (d) any other legend required by the Stockholders Agreement.

          The Company shall make a notation on its stock books regarding the
restrictions on transfer of the Warrants and Warrant Stock required by
applicable securities and other laws, this Warrant and the Warrant Agreement,
and will transfer securities on the books of the Company only to the extent not
inconsistent therewith. Without limiting the foregoing, the Company shall refuse
to register any transfer of the Warrants or Warrant Stock not made in accordance
with the registration requirements of the Act or pursuant to an applicable
exemption from registration under the Act.

     5.   Adjustment of Exercise Price; Number and Kind of Shares. The number
          -------------------------------------------------------            
and kind of shares of Warrant Stock issuable upon exercise of this Warrant (or
any shares of stock or other securities or property at the time receivable or
issuable upon exercise of this Warrant) and the Exercise Price therefor, are
subject to adjustment upon the occurrence of the following events:

          5.1.  Adjustment for Stock Splits, Stock Subdivisions or Combinations
                ---------------------------------------------------------------
of Shares. The Exercise Price of this Warrant shall be proportionally decreased
- ---------                                                                      
and the number of shares of Series A Common Stock issuable upon exercise of this
Warrant (or

                                       7
<PAGE>
 
any shares of stock or other securities at the time issuable upon exercise of
this Warrant), shall be proportionally increased to reflect any stock split or
subdivision of the Company's Series A Common Stock (or any shares of stock or
other securities at the time issuable upon exercise of this Warrant). The
Exercise Price of this Warrant shall be proportionally increased and the number
of shares of Series A Common Stock issuable upon exercise of this Warrant (or
any shares of stock or other securities at the time issuable upon exercise of
this Warrant) shall be proportionally decreased to reflect any combination of
the Company's Series A Common Stock (or any shares of stock or other securities
at the time issuable upon exercise of this Warrant) into a smaller number of
shares.

          5.2   Adjustment for Reorganization, Consolidation, Merger. In case of
                ----------------------------------------------------            
any reorganization of the Company (or of any other corporation, the stock or
other securities of which are at the time receivable on the exercise of this
Warrant), after the Issue Date, or in case, after such date, the Company (or any
such corporation) shall consolidate with or merge into another corporation or
convey all or substantially all of its assets to another corporation or other
entity, then, and in each such case, the Registered Holder of this Warrant, upon
any permitted exercise of this Warrant (as provided in Section 2), at any time
after the consummation of such reorganization, consolidation, merger, or
conveyance, shall be entitled to receive, in lieu of the stock or other
securities and property receivable upon the exercise of this Warrant prior to
such consummation, the stock or other securities or property to which such
Registered Holder would have been entitled upon the consummation of such
reorganization, consolidation, merger or conveyance if such Registered Holder
had exercised this Warrant immediately prior thereto, all subject to further
adjustment as provided in this Section 5, and the successor or purchasing
corporation or other entity in such reorganization, consolidation, merger or
conveyance (if other than the Company) shall duly execute and deliver to the
Registered Holder a supplement hereto acknowledging such corporation's or
entity's obligations under this Warrant; and in each such case, the terms of
this Warrant (including, the exercisability, transfer and adjustment provisions
of this Warrant) shall be applicable to the shares of stock or other securities
or property receivable upon the exercise of this Warrant after the consummation
of such reorganization, consolidation, merger or conveyance. The foregoing
provisions of this Section 5.2 shall similarly apply to successive
reorganizations, consolidations, mergers, sales and transfers and to the stock
or securities of any other corporation that are at the time receivable upon the
exercise of this Warrant. If the per-share consideration payable to the
Registered Holder hereof for shares in connection with any such transaction is
in a form other than cash or marketable securities, then the value of such
consideration shall be determined in good faith by the Company's Board of
Directors. In all events, appropriate adjustment (as determined in good faith by
the Company's Board of Directors) shall be made in the application of the
provisions of this Warrant with respect to the rights and interests of the
Registered Holder after the transaction, to the end that the provisions of this
Warrant shall be applicable after that event, as near as reasonably may be, in
relation to any shares or other property deliverable after that event upon
exercise of this Warrant.

                                       8
<PAGE>
 
          5.3.   Adjustment for Dividends or Distributions of Stock or Other
                 -----------------------------------------------------------
Securities or Property. In case the Company shall make or issue, or shall fix a
- ----------------------                                                         
record date for the determination of eligible Registered Holders entitled to
receive, a dividend or other distribution with respect to the Series A Common
Stock (or any shares of stock or other securities at the time issuable upon
exercise of the Warrant) payable in (a) securities of the Company or (b) assets
(excluding cash dividends paid or payable solely out of retained earnings),
then, in each such case, the Registered Holder of this Warrant on exercise
hereof at any time after the record date of such dividend or other distribution,
shall receive, in addition to the shares of Series A Common Stock (or such other
stock or securities) issuable on such exercise prior to such date, and without
the payment of additional consideration therefor, the securities or such other
assets of the Company to which such Registered Holder would have been entitled
upon such date if such Registered Holder had exercised this Warrant on the date
hereof and had thereafter, during the period from the date hereof to and
including the date of such exercise, retained such shares and/or all other
additional stock available by it as aforesaid during such period giving effect
to all adjustments called for by this Section 5 (and the Company shall place
such securities or other assets into escrow until receipt by the Registered
Holder); provided, that if any such dividend or distribution consists of the
         --------                                                           
securities of another entity controlled by the Company, the Company shall make
provision reasonably acceptable to the Registered Holder to provide the
Registered Holder with substantially the same economic benefits as if the
Registered Holder had exercised this Warrant immediately prior to such record
date and had received such securities in such dividend or distribution.

          5.4.   Reclassification. If the Company, by reclassification of
                 ----------------                                        
securities or otherwise, shall change any of the securities as to which purchase
rights under this Warrant exist into the same or a different number of
securities of any other class or classes, this Warrant shall thereafter
represent the right to acquire such number and kind of securities as would have
been issuable as the result of such change with respect to the securities that
were subject to the purchase rights under this Warrant immediately prior to such
reclassification or other change and the Exercise Price therefore shall be
appropriately adjusted, all subject to further adjustment as provided in this
Section 5.

     6.   Certificate as to Adjustments. In each case of any adjustment in
          -----------------------------                                   
either the Exercise Price or in the number of shares of Warrant Stock, or other
securities or property receivable upon the exercise of this Warrant, the Chief
Financial Officer of the Company shall promptly thereafter compute such
adjustment in accordance with the terms of this Warrant and prepare a
certificate setting forth such adjustment and showing in detail the facts upon
which such adjustment is based, including a statement of the adjusted Exercise
Price. The Company will cause copies of such certificate to be mailed (by first
class mail, postage prepaid) to the Registered Holder.

     7.   Loss or Mutilation. Upon receipt by the Company of evidence reasonably
          ------------------                                                    
satisfactory to it of the ownership, and the loss, theft, destruction or
mutilation, of this Warrant, and of indemnity reasonably satisfactory to it, and
(in the case of mutilation) 

                                       9
<PAGE>
 
upon surrender and cancellation of this Warrant, the Company will execute and
deliver in lieu thereof a new Warrant of like tenor.

     8.   Representations and Warranties of the Registered Holder.
          ------------------------------------------------------- 

          8.1   Restrictions under Securities Laws. The Registered Holder
                ----------------------------------                       
understands that neither the offer and sale of this Warrant nor the offer and
sale of shares of Warrant Stock that may be purchased upon exercise thereof have
been registered under the Act, or any state securities laws. As a condition to
the issuance of this Warrant and to its exercise the Registered Holder hereby
represents and warrants to the Company that:

          (a)  The Registered Holder is capable of evaluating the merits and
risks of any investment in the Warrant and the underlying shares of Warrant
Stock (collectively, the "Securities"), is financially capable of bearing a
total loss of this investment and either: (i) has a preexisting personal or
business relationship with the Company or its principals; (ii) by reason of the
Registered Holder's business or financial experience, has the capacity to
protect his or its own interests in connection with this investment; or (iii) if
the Registered Holder is the Initial Registered Holder, is an "accredited
investor" within the meaning of Regulation D promulgated under the Act, as
amended.

          (b)  The Registered Holder has had access to all information regarding
the Company, its present and prospective business, assets, liabilities and
financial condition that the Registered Holder considers important to making the
decision to acquire the Securities and has had ample opportunity to ask
questions of and receive answers from the Company's representatives concerning
an investment in the Securities and to obtain any and all documents requested in
order to supplement or verify any of the information supplied.

          (c)  The Registered Holder understands that the Securities shall be
deemed restricted securities under the Act and may not be resold unless they are
registered under the Act and any applicable State securities law, or in the
opinion of counsel in form and substance satisfactory to the Company, an
exemption from such registration is available.

          (d)  The Registered Holder is aware of Rule 144 promulgated under the
Act, which rule, as in effect on the date hereof, provides, in substance, that:
(i) after one year from the date restricted securities have been purchased and
fully paid for, a holder may transfer restricted securities provided certain
conditions are met (e.g., certain public information is available about the
Company), and specific limitations on the amount of shares which can be sold
within certain periods and the manner in which such shares must be sold are
complied with; and (ii) after two years from the date the securities have been
purchased and fully paid for, holders who are not "affiliates" of the Company
may sell restricted securities without satisfying such conditions.

          (e)  The Registered Holder further understands that if the
requirements of Rule 144 are not met, registration under the Act or compliance
with some 

                                       10
<PAGE>
 
other registration exemption will be required for any disposition of the
Securities; and that, although Rule 144 is not exclusive, the SEC has expressed
its opinion that persons proposing to sell restricted securities other than in a
registered offering or other than pursuant to Rule 144 will have a substantial
burden of proof in establishing that an exemption from registration is available
for such offers or sales and such persons and the brokers who participate in the
transactions do so at their own risk.

          8.2   Compliance with U.S. Securities Laws. The Registered Holder, by
                ------------------------------------                           
acceptance hereof, agrees that, absent an effective registration statement filed
with the SEC under the Act, covering the disposition or sale of the Securities
or other securities of the Company issued or issuable upon exercise hereof, as
the case may be, and registration or qualification under applicable state
securities laws, such Registered Holder will not sell, transfer, pledge, or
hypothecate any or all such Securities or other securities, as the case may be,
unless either (i) the Company has received an opinion of counsel, in form and
substance reasonably satisfactory to the Company, to the effect that such
registration is not required in connection with such disposition or (ii) the
sale of such Securities and/or securities is made pursuant to SEC Rule 144.

     9.   No Rights or Liabilities as Stockholder. This Warrant does not by
          ---------------------------------------                          
itself entitle the Registered Holder to any voting rights or other rights as a
stockholder of the Company. In the absence of affirmative action by the
Registered Holder to purchase Warrant Stock by exercise of this Warrant, no
provisions of this Warrant, and no enumeration herein of the rights or
privileges of the Registered Holder, shall cause such Registered Holder to be a
stockholder of the Company for any purpose.

     10.   Regulatory Compliance. The Company and the Registered Holder hereby
           ---------------------                                              
acknowledge that exercise of this Warrant by the Registered Holder is subject to
receipt of all necessary governmental consents and approvals and may subject the
Company and/or the Registered Holder to the filing requirements of the Hart-
Scott-Rodino Antitrust Improvements Act of 1976, as amended (the "HSR Act"), and
that the Registered Holder may be prevented from exercising this Warrant until
receipt of all necessary governmental consents and approvals and the expiration
or early termination of all waiting periods imposed by the HSR Act.  Promptly
following the Registered Holder's notice of exercise or other written request
from the Registered Holder, the Company and the Registered Holder will use their
respective commercially reasonable efforts to make all filings necessary to
obtain such consents and approvals and/or to cause the expiration or termination
of any applicable waiting period under the HSR Act.  In the event that the
Registered Holder has been unable to exercise this Warrant prior to the
Expiration Date because of the failure to receive a governmental consent or
approval or the failure of the waiting period under the HSR Act to have expired
or have terminated (despite the Registered Holder's and the Company's continuing
use of commercially reasonable efforts to obtain such consent or approval or the
expiration or termination of such waiting period), then CSC or the Initial
Registered Holder, as the case may be, shall have the right to acquire upon
exercise on the Expiration Date of the then-remaining unexercised portion of
this Warrant shares of a series or class of non-voting, transferable, equity

                                       11
<PAGE>
 
securities of the Company that are convertible at any time into the number of
shares of Warrant Stock that CSC or the Initial Registered Holder would have
obtained upon exercise of this Warrant immediately prior thereto and upon
payment of the aggregate Exercise Price that would have been so payable; and the
Company will take such steps as may be necessary to effect the creation,
authorization and issuance of such securities. The terms of such securities will
be designed to provide the same economic benefits as the Warrant Stock.

     11.  Severability. If any term, provision, covenant or restriction of this
          ------------                                                         
Warrant is held by a court of competent jurisdiction to be invalid, void or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions of this Warrant shall remain in full force and effect and shall in
no way be affected, impaired or invalidated.

     12.  No Inconsistent Agreements. The Company will not on or after the date
          --------------------------                                           
of this Warrant enter into any agreement with respect to its securities which is
inconsistent with the rights granted to the Registered Holder of this Warrant or
otherwise conflicts with the provisions hereof. The rights granted to the
Registered Holder hereunder do not in any way conflict with and are not
inconsistent with the rights granted to a registered holder of the Company's
securities under any other agreements, except rights that have been waived.

     13.  Headings. The headings in this Warrant are for purposes of
          --------                                                  
convenience in reference only, and shall not be deemed to constitute a part
hereof.

     14.  Law Governing. This Warrant shall be construed and enforced in
          -------------                                                 
accordance with, and governed by, the internal laws of the State of Delaware,
excluding that body of law applicable to conflicts of laws.

     15.  Terms Binding. By acceptance of this Warrant, the Registered Holder of
          -------------                                                         
this Warrant (and each subsequent assignee, transferee or Registered Holder of
this Warrant) accepts and agrees to be bound by all the terms and conditions of
this Warrant.

     16.  Counterparts. This Warrant may be executed in one or more
          ------------                                             
counterparts, each of which shall be an original and all of which together shall
constitute one and the same instrument.

                                       12
<PAGE>
 
IN WITNESS WHEREOF, the Company and the Registered Holder have executed this
Warrant as of the Issue Date.

THE COMPANY:                        ACKNOWLEDGED AND ACCEPTED
                                    BY REGISTERED HOLDER:

AT HOME CORPORATION                 CSC PARENT
CORPORATION


By:                                 By:
   -----------------------------        --------------------------------

Name:                               Name:
     ---------------------------         -------------------------------

Title:                              Title:
      --------------------------          ------------------------------

                           [WARRANT SIGNATURE PAGE]

                                       13
<PAGE>
 
                                                                       Exhibit 1
                                                                       ---------
                              FORM OF SUBSCRIPTION
                              --------------------

                  (To be signed only upon exercise of Warrant)

To:  At Home Corporation
     425 Broadway
     Redwood City, California 94063
     Attention: President

cc:  Fenwick & West LLP
     Two Palo Alto Square
     Palo Alto, CA 94306
     Attention: Gordon K. Davidson, Esq.

     (1) The undersigned hereby elects to purchase _______ shares of Series A
Common Stock of At Home Corporation, a Delaware corporation (the "Company") (or
                                                                  -------
such other class or series of capital stock of the Company or any successor
thereto into which the Series A Common Stock has been converted (describe:
_____________)) or other securities of the Company issuable pursuant to Section
10 of the attached Warrant (describe: _____________) (collectively, "Applicable
                                                                     ----------
Securities"), all pursuant to the terms of the attached Warrant, and tenders
- ----------
herewith payment of the purchase price for such shares in full.

     (2)  In exercising this Warrant, the undersigned hereby confirms and
acknowledges that the representations and warranties of the Undersigned set
forth in Section 8 of the Warrant are true and correct as of this date.

     (3)  Please issue a certificate or certificates representing said shares of
Applicable Securities in the name specified below:


                              ------------------------------------
                              (Name)


                              ------------------------------------
                              (Address)


                              ------------------------------------
                              (City, State, Zip Code)


     (4)  Please issue a new Warrant for the unexercised portion of the attached
Warrant in the name of the undersigned or in such other name as is specified
below:



 

                                       14
<PAGE>
 
- ---------------------------------
(Other Name)

     (5) The certification of the undersigned required pursuant to Section 2.1
of the Warrant is attached as Annex A hereto.
                              -------        


                              REGISTERED HOLDER



                              ----------------------------------------
                              (Name of Registered Holder)


                              ----------------------------------------
                              (Signature of Registered Holder)


                              ----------------------------------------
                              (Title)


                              ----------------------------------------
                              (Date)

                                       15
<PAGE>
 
                                                                       Exhibit 2
                                                                       ---------
                               FORM OF ASSIGNMENT
                               ------------------
                                        
     FOR VALUE RECEIVED, the undersigned Registered Holder of the attached
Warrant hereby sells, assigns and transfers unto each of the Assignee(s) named
below all of the rights of the undersigned under such Warrant, with respect to
that number, class and series of shares of Warrant Stock set forth below:

                                              Number, Class and
                                              Series of Shares of
Name of Assignee       Address                Warrant Stock Affected
- ----------------       -------                ----------------------



and does hereby irrevocably constitute and appoint the Secretary of At Home
Corporation, a Delaware corporation (the "Company") as attorney to make such
                                          -------
transfer on the books of the Company maintained for such purpose, with full
power of substitution in the premises.

Dated:

                              REGISTERED HOLDER

                              Name of Registered Holder:


 
                              ----------------------------------

                              By:
                                 -------------------------------

                              Name:
                                   -----------------------------

                              Title:
                                    ----------------------------

                                       16


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