BARON ASSET FUND
NSAR-B, 1998-11-27
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<PAGE>      PAGE  1
000 B000000 09/30/98
000 C000000 0000810902
000 D000000 N
000 E000000 NF
000 F000000 Y
000 G000000 N
000 H000000 N
000 I000000 3.0.a
000 J000000 A
001 A000000 BARON ASSET FUND
001 B000000 811-5032
001 C000000 2125832000
002 A000000 767 FIFTH AVENUE  49TH FLOOR
002 B000000 NEW YORK
002 C000000 NY
002 D010000 10153
003  000000 N
004  000000 N
005  000000 N
006  000000 N
007 A000000 Y
007 B000000  3
007 C010100  1
007 C020100 BARON ASSET FUND
007 C030100 N
007 C010200  2
007 C020200 BARON GROWTH & INCOME FUND
007 C030200 N
007 C010300  3
007 C020300 BARON SMALL CAP FUND
007 C030300 N
007 C010400  4
007 C010500  5
007 C010600  6
007 C010700  7
007 C010800  8
007 C010900  9
007 C011000 10
008 A00AA01 BAMCO, INC.
008 B00AA01 A
008 C00AA01 801-29080
008 D01AA01 NEW YORK
008 D02AA01 NY
008 D03AA01 10153
011 A00AA01 BARON CAPITAL, INC.
011 B00AA01 8-27533
011 C01AA01 NEW YORK
011 C02AA01 NY
011 C03AA01 10153
012 A00AA01 DST SYSTEMS, INC.
012 B00AA01 84-00448
<PAGE>      PAGE  2
012 C01AA01 KANSAS CITY
012 C02AA01 MO
012 C03AA01 84105
013 A00AA01 PRICEWATERHOUSECOOPERS, LLP
013 B01AA01 NEW YORK
013 B02AA01 NY
013 B03AA01 10019
013 B04AA01 6013
014 A00AA01 BARON CAPITAL, INC.
014 B00AA01 8-27533
015 A00AA01 THE BANK OF NEW YORK
015 B00AA01 C
015 C01AA01 NEW YORK
015 C02AA01 NY
015 C03AA01 10286
015 E01AA01 X
018  00AA00 Y
019 A00AA00 N
019 B00AA00    0
020 A000001 BARON CAPITAL, INC.
020 B000001 13-3107580
020 C000001   5433
020 A000002 GOLDMAN SACHS
020 B000002 13-5515160
020 C000002    287
020 A000003 KALB VOORHIS
020 B000003 13-5549000
020 C000003    251
020 A000004 BEAR STEARNS
020 B000004 13-3604093
020 C000004    247
020 A000005 MORGAN STANLEY
020 B000005 13-2655998
020 C000005    246
020 A000006 BT ALEX BROWN & CO.
020 B000006 52-1319768
020 C000006    156
020 A000007 LEHMAN BROTHERS
020 B000007 13-2518466
020 C000007    135
020 A000008 MONTGOMERY SECURITIES
020 B000008 94-1701676
020 C000008    130
020 A000009 FIRST BOSTON
020 B000009 13-5659485
020 C000009    118
020 A000010 DONALDSON, LUFKIN & JENRETTE
020 B000010 13-2741729
020 C000010    113
021  000000     8136
022 A000001 BEAR STEARNS
<PAGE>      PAGE  3
022 B000001 13-3604093
022 C000001    203254
022 D000001    106415
022 A000002 MERRILL LYNCH & CO
022 B000002 13-5674085
022 C000002    133350
022 D000002     65303
022 A000003 GOLDMAN SACHS
022 B000003 13-5515160
022 C000003    132699
022 D000003     32679
022 A000004 LEHMAN BROTHERS
022 B000004 13-2518466
022 C000004    107566
022 D000004     27064
022 A000005 FIRST BOSTON
022 B000005 13-5659485
022 C000005    108926
022 D000005      2103
022 A000006 BT ALEX BROWN
022 B000006 52-1319768
022 C000006     70529
022 D000006     18653
022 A000007 MONTGOMERY SECURITIES
022 B000007 94-1701676
022 C000007     49645
022 D000007     33540
022 A000008 SMITH BARNEY SHEARSON
022 B000008 13-1912900
022 C000008     52213
022 D000008     16719
022 A000009 HERZOG
022 B000009 13-4955436
022 C000009     36116
022 D000009     32092
022 A000010 SPEAR, LEEDS & KELLOGG
022 B000010 13-3194448
022 C000010     34193
022 D000010     33996
023 C000000    1359287
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<PAGE>      PAGE  4
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<PAGE>      PAGE  5
049  00AA00 N
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<PAGE>      PAGE  6
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<PAGE>      PAGE  7
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066 A000100 Y
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066 F000100 N
066 G000100 N
067  000100 N
068 A000100 N
068 B000100 N
069  000100 N
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070 B010100 Y
070 B020100 N
070 C010100 N
070 C020100 N
070 D010100 N
070 D020100 N
070 E010100 N
070 E020100 N
070 F010100 N
070 F020100 N
070 G010100 N
070 G020100 N
070 H010100 N
070 H020100 N
070 I010100 N
070 I020100 N
070 J010100 Y
070 J020100 Y
070 K010100 Y
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070 L020100 Y
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<PAGE>      PAGE  8
070 O020100 N
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070 R020100 N
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<PAGE>      PAGE  9
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076  000100     0.00
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028 B010200     17187
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028 B030200         0
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028 C010200     12232
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028 C030200         0
028 C040200     23475
028 D010200     11791
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028 D040200     29375
028 E010200      8048
028 E020200         0
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028 E040200     35423
028 F010200     10045
<PAGE>      PAGE  10
028 F020200         0
028 F030200         0
028 F040200     27516
028 G010200     87570
028 G020200         0
028 G030200         0
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028 H000200         0
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043  000200   1078
044  000200     71
066 A000200 Y
066 B000200 N
066 C000200 N
066 D000200 N
066 E000200 Y
066 F000200 N
066 G000200 N
067  000200 N
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068 B000200 N
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070 A010200 Y
070 A020200 N
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070 B020200 N
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070 C020200 N
070 D010200 Y
070 D020200 N
070 E010200 N
070 E020200 N
070 F010200 N
070 F020200 N
070 G010200 N
070 G020200 N
070 H010200 N
070 H020200 N
070 I010200 N
070 I020200 N
070 J010200 Y
070 J020200 Y
070 K010200 Y
070 K020200 N
<PAGE>      PAGE  11
070 L010200 Y
070 L020200 Y
070 M010200 N
070 M020200 N
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<PAGE>      PAGE  12
073 A010200   0.0170
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<PAGE>      PAGE  13
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066 A000300 Y
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070 B020300 Y
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070 D010300 Y
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070 E010300 N
070 E020300 N
070 F010300 N
070 F020300 N
070 G010300 N
070 G020300 N
070 H010300 N
<PAGE>      PAGE  14
070 H020300 N
070 I010300 N
070 I020300 N
070 J010300 Y
070 J020300 Y
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<PAGE>      PAGE  15
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SIGNATURE   LINDA S. MARTINSON                           
TITLE       GENERAL COUNSEL     
 


<TABLE> <S> <C>

<ARTICLE>          6
<CIK>              0000810902
<NAME>             BARON ASSET FUND
<SERIES>
   <NUMBER>        1
   <NAME>          BARON ASSET FUND
       
<S>                                    <C>
<PERIOD-TYPE>                          YEAR
<FISCAL-YEAR-END>                      SEP-30-1998
<PERIOD-START>                         OCT-01-1997
<PERIOD-END>                           SEP-30-1998
<INVESTMENTS-AT-COST>                  $ 4,376,808,032
<INVESTMENTS-AT-VALUE>                 $ 4,399,181,818
<RECEIVABLES>                          $    30,287,932
<ASSETS-OTHER>                         $     5,255,886
<OTHER-ITEMS-ASSETS>                                 0
<TOTAL-ASSETS>                         $ 4,434,725,636
<PAYABLE-FOR-SECURITIES>               $    23,179,523
<SENIOR-LONG-TERM-DEBT>                              0
<OTHER-ITEMS-LIABILITIES>              $     1,039,665
<TOTAL-LIABILITIES>                    $    24,219,188
<SENIOR-EQUITY>                                      0
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<SHARES-COMMON-STOCK>                      110,366,720
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<NET-INVESTMENT-INCOME>                $     5,182,423
<REALIZED-GAINS-CURRENT>               $(   76,452,243)
<APPREC-INCREASE-CURRENT>              $(  848,684,103)
<NET-CHANGE-FROM-OPS>                  $(  919,953,923)
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</TABLE>

<TABLE> <S> <C>

<ARTICLE>          6
<CIK>              0000810902
<NAME>             BARON ASSET FUND
<SERIES>
   <NUMBER>        2
   <NAME>          BARON GROWTH & INCOME FUND
       
<S>                                    <C>
<PERIOD-TYPE>                          YEAR
<FISCAL-YEAR-END>                      SEP-30-1998
<PERIOD-START>                         OCT-01-1997
<PERIOD-END>                           SEP-30-1998
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<INVESTMENTS-AT-VALUE>                 $   314,824,552
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<OTHER-ITEMS-ASSETS>                   $         8,218
<TOTAL-ASSETS>                         $   325,408,685
<PAYABLE-FOR-SECURITIES>               $     1,347,751
<SENIOR-LONG-TERM-DEBT>                              0
<OTHER-ITEMS-LIABILITIES>              $     8,503,084
<TOTAL-LIABILITIES>                    $     9,850,835
<SENIOR-EQUITY>                                      0
<PAID-IN-CAPITAL-COMMON>               $   282,019,889
<SHARES-COMMON-STOCK>                       15,527,447
<SHARES-COMMON-PRIOR>                       15,702,090
<ACCUMULATED-NII-CURRENT>              $       472,714
<OVERDISTRIBUTION-NII>                               0
<ACCUMULATED-NET-GAINS>                $(    5,890,637)
<OVERDISTRIBUTION-GAINS>                             0
<ACCUM-APPREC-OR-DEPREC>               $    38,955,884
<NET-ASSETS>                           $   315,557,850
<DIVIDEND-INCOME>                      $     6,407,337
<INTEREST-INCOME>                      $       591,891
<OTHER-INCOME>                         $        47,659
<EXPENSES-NET>                         $     6,146,997
<NET-INVESTMENT-INCOME>                $       899,890
<REALIZED-GAINS-CURRENT>               $(    6,952,711)
<APPREC-INCREASE-CURRENT>              $(   73,445,498)
<NET-CHANGE-FROM-OPS>                  $(   79,498,319)
<EQUALIZATION>                                       0
<DISTRIBUTIONS-OF-INCOME>              $(      282,139)
<DISTRIBUTIONS-OF-GAINS>               $(      929,398)
<DISTRIBUTIONS-OTHER>                                0
<NUMBER-OF-SHARES-SOLD>                      9,436,383 
<NUMBER-OF-SHARES-REDEEMED>             (    9,658,984)
<SHARES-REINVESTED>                             47,958
<NET-CHANGE-IN-ASSETS>                 $(   75,274,011)
<ACCUMULATED-NII-PRIOR>                $       285,821
<ACCUMULATED-GAINS-PRIOR>              $     1,560,614 
<OVERDISTRIB-NII-PRIOR>                              0
<OVERDIST-NET-GAINS-PRIOR>                           0
<GROSS-ADVISORY-FEES>                  $     4,310,057
<INTEREST-EXPENSE>                             232,119
<GROSS-EXPENSE>                        $     6,146,997
<AVERAGE-NET-ASSETS>                   $   430,683,885
<PER-SHARE-NAV-BEGIN>                  $         24.89 
<PER-SHARE-NII>                        $          0.06
<PER-SHARE-GAIN-APPREC>                $(         4.56)
<PER-SHARE-DIVIDEND>                   $(         0.02)
<PER-SHARE-DISTRIBUTIONS>              $(         0.05)
<RETURNS-OF-CAPITAL>                                 0
<PER-SHARE-NAV-END>                    $         20.32
<EXPENSE-RATIO>                                 0.014
<AVG-DEBT-OUTSTANDING>                               0  
<AVG-DEBT-PER-SHARE>                                 0
        

</TABLE>

<TABLE> <S> <C>

<ARTICLE>          6
<CIK>              0000810902
<NAME>             BARON ASSET FUND
<SERIES>
   <NUMBER>        3
   <NAME>          BARON SMALL CAP FUND
       
<S>                                    <C>
<PERIOD-TYPE>                          YEAR
<FISCAL-YEAR-END>                      SEP-30-1998
<PERIOD-START>                         OCT-01-1997
<PERIOD-END>                           SEP-30-1998
<INVESTMENTS-AT-COST>                  $   478,634,266
<INVESTMENTS-AT-VALUE>                 $   403,116,276
<RECEIVABLES>                          $     2,397,204
<ASSETS-OTHER>                         $        23,179
<OTHER-ITEMS-ASSETS>                                 0
<TOTAL-ASSETS>                         $   405,536,659
<PAYABLE-FOR-SECURITIES>               $     1,510,180
<SENIOR-LONG-TERM-DEBT>                              0
<OTHER-ITEMS-LIABILITIES>              $       298,481
<TOTAL-LIABILITIES>                    $     1,808,661
<SENIOR-EQUITY>                                      0
<PAID-IN-CAPITAL-COMMON>               $   506,138,465
<SHARES-COMMON-STOCK>                       46,886,613
<SHARES-COMMON-PRIOR>                                0
<ACCUMULATED-NII-CURRENT>              $             0
<OVERDISTRIBUTION-NII>                               0
<ACCUMULATED-NET-GAINS>                $(   26,892,477)
<OVERDISTRIBUTION-GAINS>                             0
<ACCUM-APPREC-OR-DEPREC>               $(   75,517,990)
<NET-ASSETS>                           $   403,727,998
<DIVIDEND-INCOME>                      $     1,729,757
<INTEREST-INCOME>                      $     1,395,050
<OTHER-INCOME>                         $     1,687,592
<EXPENSES-NET>                         $     5,638,915
<NET-INVESTMENT-INCOME>                $(      826,516)
<REALIZED-GAINS-CURRENT>               $(   26,895,646)
<APPREC-INCREASE-CURRENT>              $(   75,517,990)
<NET-CHANGE-FROM-OPS>                  $(  103,240,152)
<EQUALIZATION>                                       0
<DISTRIBUTIONS-OF-INCOME>                            0
<DISTRIBUTIONS-OF-GAINS>                             0
<DISTRIBUTIONS-OTHER>                                0
<NUMBER-OF-SHARES-SOLD>                     65,055,206 
<NUMBER-OF-SHARES-REDEEMED>             (   18,168,593)
<SHARES-REINVESTED>                                  0
<NET-CHANGE-IN-ASSETS>                 $   403,727,998
<ACCUMULATED-NII-PRIOR>                              0
<ACCUMULATED-GAINS-PRIOR>                            0 
<OVERDISTRIB-NII-PRIOR>                              0
<OVERDIST-NET-GAINS-PRIOR>                           0
<GROSS-ADVISORY-FEES>                  $     4,041,420
<INTEREST-EXPENSE>                                   0
<GROSS-EXPENSE>                        $     5,638,915
<AVERAGE-NET-ASSETS>                   $   404,866,978
<PER-SHARE-NAV-BEGIN>                  $         10.00 
<PER-SHARE-NII>                        $(         0.02)
<PER-SHARE-GAIN-APPREC>                $(         1.37)
<PER-SHARE-DIVIDEND>                                 0
<PER-SHARE-DISTRIBUTIONS>                            0
<RETURNS-OF-CAPITAL>                                 0
<PER-SHARE-NAV-END>                    $          8.61
<EXPENSE-RATIO>                                  0.139 
<AVG-DEBT-OUTSTANDING>                               0  
<AVG-DEBT-PER-SHARE>                                 0
        

</TABLE>


                        PRICEWATERHOUSECOOPERS, L.L.P.
                        1301 Avenue of the Americas
                        New York, NY 10019-6013
                        Tel: 212-259-1000
                        Fax: 212-259-1301

                        REPORT OF INDEPENDENT ACCOUNTANTS

To the Shareholders and Board of Trustees
of Baron Asset Fund:

In planning and performing our audit of the financial statements and financial
highlights of Baron Asset Fund (comprising, respectively, Baron Asset Fund,
Baron Growth and Income, and Baron Small Cap), for the year ended
September 30, 1998, we considered its internal control, including control over
safeguarding securities, in order to determine our auditing procedures for the
purpose of expressing our opinion on the financial statements and financial
highlights and to comply with the requirements for Form N-SAR, not to provide
assurance on internal control.

The management of Baron Asset Fund is responsible for establishing and
maintaining internal control.  In fulfilling this responsibility, estimates
and
judgements by management are required to assess the expected benefits and
related costs of controls.  Generally, controls that are relevant to an audit
pertain to the entity's objective of preparing financial statements and
financial highlights for external purposes that are fairly presented in
conformity with generally accepted accounting principles.  Those controls
include the safeguarding of assets against unauthorized acquisition, use or
disposition.

Because of inherent limitations in internal controls, errors or fraud may
occur
and may not be detected.  Also, projection of any evaluation of internal
control to future periods is subject to the risk that it may become inadequate
because of changes in conditions or that the effectiveness of the design and
operation may deteriorate.

Our consideration of internal control would not necessarily disclose all
matters in internal control that might be material weaknesses under standards
established by the American Institute of Certified Public Accountants.  A
material weakness is a condition in which the design or operation of any
specific internal control component does not reduce to a relatively low level
the risk that errors or fraud in amounts that would be material in relation to
the financial statements and financial highlights being audited may occur and
not be detected within in timely period by employees in the normal course of
performing their assigned functions.  However, we noted no matters involving
internal control, including controls over safeguarding securities, that we
consider to be material weaknesses as defined above as of September 30, 1998.

This report is intended solely for the information and use of management and
the Securities and Exchange Commission.

                                            /s/ PricewaterhouseCoopers, LLP
                                            -------------------------------
                                                PricewaterhouseCoopers, LLP

New York, New York
November 23, 1998



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