UNITED STATES                       OMB APPROVAL

        SECURITIES AND EXCHANGE COMMISSION        OMB Number: 3235-0456

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               WASHINGTON, D.C. 20549             Estimated average burden
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                    FORM 24F-2

        Annual Notice of Securities Sold
             Pursuant to Rule 24f-2

     Read instructions at end of Form before preparing Form.


1.   Name and address of issuer:

     Baron Asset Fund, a series fund (the "Trust")

     767 Fifth Avenue
     New York, NY 10153



2.   The name of each series or class of securities for which this Form is filed
     (If the Form is being filed for all series and classes of securities of the
     issuer, check the box but do not list series or classes):



3.   Investment Company Act File Number:

     Securities Act File Number:   811-5032

     Securities Act File Number:   33-12112



4.   (a)  Last day of fiscal year for which this notice is filed:

          September 30, 1999

4.   (b)  [ ]Check  box if this Form is being  filed  late  (i.e.,  more than 90
             calendar days after the end of the issuer's fiscal year). (See
             Instruction A.2)

      Note: If the  Form  is  being  filed  late,  interest  must be paid on the
            registration fee due.

4.   (c)  Check box if this is the last time the issuer will be filing this
          Form.


5.   Calculation of registration fee:

     (i)   Aggregate sale price of securities sold
           during the fiscal year pursuant to
           section 24(f):                                        $ 2,929,733,920

     (ii)  Aggregate price of shares redeemed
           or repurchased during the fiscal year: $2,619,785,774

     (iii) Aggregate price of shares redeemed
           or repurchased during any prior fiscal
           year ending no earlier than October 11,
           1995 that were not previously used to
           reduce registration fees payable to the
           Commission:                            $            0

     (iv)  Total available redemption credits [add
           Items 5(ii) and 5(iii)]:                             - $2,619,785,774
                                                              ------------------
     (v)   Net sales - - if Item 5(i) is greater
           than Item 5(iv) [subtract Item 5(iv)
           from Item 5(i)]:                                     $    309,948,146

     (vi)  Redemption credits available for use in $         (0)
           future years - - if Item 5(i) is less ---------------
           than Item 5(iv) [subtract Item 5(iv)
           from Item 5(i)]:

     (vii) Multiplier for determining registration
           fee (See Instruction C.9):                         x         0.000278
                                                              ------------------
     (viii)Registration fee due [multiply Item
           5(v) by Item 5(vii)] (enter "0" if no
           fee is due):                                       $        86,165.58
                                                                      ==========



6.   Prepaid Shares

     If the  response  to Item 5(i) was  determined  by  deducting  an amount of
     securities that were  registered  under the Securities Act of 1933 pursuant
     to rule 24e-2 as in effect before October 11, 1997,  then report the amount
     of securities (number of shares or other units) deducted here:  __________.
     If there is a number of shares or other units that were registered pursuant
     to rule 24e-2 remaining unsold at the end of the fiscal year for which this
     form is filed that are  available  for use by the  issuer in future  fiscal
     years, then state that number here: __________.



7.   Interest  due - - if this Form is being  filed  more than 90 days after the
     end of the issuer's fiscal year (see Instruction D):                  + $ 0



8.   Total of the amount of the registration fee due plus any interest due [line
     5(viii) plus line 7]:                                         = $ 86,165.58


9.   Date  the  registration  fee  and  any  interest  payment  was  sent to the
     Commission's lockbox depository:

          Method of Delivery:

             [X]    Wire Transfer

             [ ]    Mail or other means



                                 SIGNATURES

This  report has been  signed  below by the  following  persons on behalf of the
issuer and in the capacities and on the dates indicated.



By: (Signature and Title)     *  /s/ Linda S. Martinson
                                 ----------------------
                                     Linda S.  Martinson
                                     Vice President and General Counsel

Date:     November 29, 1999

    *Please print the name and title of the signing officer below the signature.