<PAGE>   1
                                                                     EXHIBIT 4.4

                          REGISTRATION RIGHTS AGREEMENT

                                                                   July 31, 1998

To the several persons listed
in Schedule I attached hereto:

Ladies and Gentlemen:

                  This will confirm that in consideration of the acquisition on
the date hereof (the "Closing Date") by the several persons listed on Schedule I
hereto of an aggregate 11,860,571 shares of Common Stock, $.01 par value per
share, of MedCath Holdings, Inc., a Delaware corporation (the "Company"), in
exchange for their respective contributions of cash and/or shares of common
stock of MedCath Incorporated ("MedCath"), pursuant to (i) the Contribution
Agreement dated as of the date hereof (the "Contribution Agreement") among the
Company and the several persons named in Schedule I thereto and (ii) a
Subscription Agreement between certain physicians and the Company, and as an
inducement to them to consummate the transactions contemplated by the
Contribution Agreement, the Company hereby covenants and agrees with each of
you, and with each subsequent holder of Restricted Stock (as such term is
defined herein) as follows:

                  1.       Certain Definitions. As used herein, the following
terms shall have the following respective meanings:

                  "Common Stock" shall mean the Common Stock, $.01 par value per
share, of the Company, as constituted as of the date of this Agreement, subject
to adjustment pursuant to the provisions of Section 8 hereof.

                  "Commission" shall mean the Securities and Exchange
Commission, or any other federal agency at the time administering the Securities
Act.

                  "Exchange Act" shall mean the Securities Exchange Act of 1934
or any similar federal statute, and the rules and regulations of the Commission
thereunder, all as the same shall be in effect at the time.
<PAGE>   2

                  "KKR Shares" shall mean the shares of Common Stock received in
exchange on the date hereof pursuant to the Contribution Agreement by MedCath
1998 LLC ("KKR Fund").

                  "Registration Expenses" shall mean the expenses so described
in Section 6 hereof.

                  "Restricted Stock" shall mean any shares of capital stock of
the Company, the certificates for which are required to bear the legend set
forth in Section 2 hereof.

                  "Securities Act" shall mean the Securities Act of 1933 or any
similar federal statute, and the rules and regulations of the Commission
thereunder, all as the same shall be in effect at the time.

                  "Selling Expenses" shall mean the expenses so described in
Section 6 hereof.

                  "WCAS Shares" shall mean the shares of Common Stock received
in exchange on the date hereof pursuant to the Contribution Agreement by the
persons listed on Schedule I hereto under the heading "WCAS Stockholders."

                  2. Restrictive Legend. Each certificate representing the KKR
Shares and the WCAS Shares, and each certificate issued upon exchange or
transfer of any of such securities, as the case may be, other than in a public
sale or as otherwise permitted pursuant to any stockholders' agreement affecting
such shares, shall be stamped or otherwise imprinted with a legend substantially
in the following form:

                  "THE SHARES REPRESENTED BY THIS CERTIFICATE
                  HAVE NOT BEEN REGISTERED UNDER THE
                  SECURITIES ACT OF 1933, AS AMENDED, AND MAY
                  NOT BE SOLD, TRANSFERRED OR OTHERWISE
                  DISPOSED OF UNLESS THEY HAVE BEEN REGISTERED
                  UNDER THAT ACT OR AN EXEMPTION FROM
                  REGISTRATION IS AVAILABLE."

                  3.       Required Registration.

                  (a)      At any time, either of WCAS VII (on behalf of the
WCAS Stockholders) or KKR Fund may request the Company to register under the
Securities Act all or any portion of the Restricted Stock held by such
requesting holder or holders for sale in the manner specified in such notice;
provided, however, that the only securities which the Company shall be required
to register pursuant hereto shall be shares of Common Stock.

                  (b)      Subject to Section 2(a)(v) of the Stockholders'
Agreement among the Company, KKR Fund and the WCAS Stockholders (listed on
Schedule I hereto), promptly following receipt of any notice under paragraph
3(a) above, the Company shall immediately notify any holders of Restricted Stock
from whom notice has not been received and shall use its best


                                       2
<PAGE>   3

efforts to register under the Securities Act, for public sale in accordance with
the method of disposition specified in such notice from requesting holders, the
number of shares of Restricted Stock specified in such notice (and in any
notices received from other holders of Restricted Stock within 20 days after
their receipt of such notice from the Company); provided, however, that if a
proposed registration involves an underwritten offering and the managing
underwriter advises the Company in writing that, in its opinion, the number of
shares of Common Stock requested to be included in the proposed registration
exceeds that number which can be sold in such offering, so as to be likely to
have an adverse effect on the price, timing or distribution of the shares of
Common Stock offered in such offering as contemplated by the Company, then the
Company will include in the proposed registration (i) first, 100% of the shares
of Common Stock the Company proposes to sell and (ii) second, to the extent of
the number of shares of Common Stock requested to be included in such
registration which, in the opinion of such managing underwriter, can be sold
without having the adverse effect referred to above, the number of shares of
Common Stock that holders of Restricted Stock have requested to be included in
the proposed registration, such amount to be allocated pro rata among all
requesting holders on the basis of the relative number of shares of Common Stock
then held by each such holder (provided that any shares thereby allocated to any
such holder that exceed such holder's request will be reallocated among the
remaining requesting holders in like manner). If such method of disposition
shall be an underwritten public offering, the selling holders of at least
two-thirds of the Restricted Stock included in the offering may designate the
managing underwriter of such offering, subject to the approval of the Company,
which approval shall not be unreasonably withheld. The Company shall be
obligated to register Restricted Stock pursuant to this paragraph 3(b) on six
occasions (with respect to requests by KKR Fund) and five occasions (with
respect to requests by WCAS VII) only and each demand shall request registration
of at least 15% of the amount of Restricted Stock held by the requesting party
and its affiliates as of the date hereof. Notwithstanding anything to the
contrary contained herein, the obligation of the Company under this paragraph
3(b) shall be deemed satisfied only when a registration statement covering all
shares of Restricted Stock specified in notices received as aforesaid, for sale
in accordance with the method of disposition specified by the requesting holder,
shall have become effective and, if such method of disposition is a firm
commitment underwritten public offering, all such shares shall have been sold
pursuant thereto.

                  (c)      The Company shall be entitled to include in any
registration statement referred to in this Section 3, for sale in accordance
with the method of disposition specified by the requesting holders, shares of
Common Stock to be sold by the Company for its own account, except as and to the
extent that, in the opinion of the managing underwriter (if such method of
disposition shall be an underwritten public offering), such inclusion would
adversely affect the marketing of the Restricted Stock to be sold. Except as
provided in this paragraph (c), the Company will not effect any other
registration of its Common Stock, whether for its own account or that of other
holders, from the date of receipt of a notice from requesting holders pursuant
to this Section 3 until the completion of the period of distribution of the
registration contemplated thereby.


                                       3
<PAGE>   4

                  4.       Incidental Registration. If the Company at any time
(other than pursuant to Section 3 hereof) proposes to register any of its Common
Stock under the Securities Act for sale to the public, whether for its own
account or for the account of other securityholders or both (except with respect
to registration statements on Form S-4 or S-8 or another form not available for
registering the Restricted Stock for sale to the public), it will give written
notice at such time to all holders of outstanding Restricted Stock of its
intention to do so. Upon the written request of any such holder, given within
twenty (20) days after receipt of any such notice by the Company, to register
any of its Restricted Stock (which request shall state the intended method of
disposition thereof), the Company will use its best efforts to cause the
Restricted Stock, as to which registration shall have been so requested, to be
included in the securities to be covered by the registration statement proposed
to be filed by the Company, all to the extent requisite to permit the sale or
other disposition by the holder (in accordance with its written request) of such
Restricted Stock so registered; provided, however, that nothing herein shall
prevent the Company from abandoning or delaying such registration at any time;
provided, further, however, that the only securities which the Company shall be
required to register pursuant hereto shall be shares of Common Stock. In the
event that any registration pursuant to this Section 4 shall be, in whole or in
part, an underwritten public offering of Common Stock, any request by a holder
pursuant to this Section 4 to register Restricted Stock shall specify that such
Restricted Stock is to be included in the underwriting on the same terms and
conditions as the shares of Common Stock otherwise being sold through
underwriters under such registration. If a proposed registration involves an
underwritten offering and the managing underwriter advises the Company in
writing that, in its opinion the number of shares of Common Stock requested to
be included in the proposed registration exceeds that number which can be sold
in such offering, so as to be likely to have an adverse effect on the price,
timing or distribution of the shares of Common Stock offered in such offering as
contemplated by the Company, then the Company will include in the proposed
registration (i) first, 100% of the shares of Common Stock the Company proposes
to sell and (ii) second, to the extent of the number of shares of Common Stock
requested to be included in such registration which, in the opinion of such
managing underwriter, can be sold without having the adverse effect referred to
above, the number of shares of Common Stock that holders of Restricted Stock
have requested to be included in the proposed registration, such amount to be
allocated pro rata among all requesting holders on the basis of the relative
number of shares of Common Stock then held by each such holder (provided that
any shares thereby allocated to any such holder that exceed such holder's
request will be reallocated among the remaining requesting holders in like
manner).

                  Notwithstanding anything to the contrary contained in this
Agreement, in the event that there is a firm commitment underwritten public
offering of securities of the Company pursuant to a registration covering
Restricted Stock and a holder of Restricted Stock does not elect to sell his
Restricted Stock to the underwriters of the Company's securities in connection
with such offering, such holder shall refrain from selling such Restricted Stock
during the period of distribution of the Company's securities by such
underwriters and the period in which the underwriting syndicate participates in
the after market; provided, however, that such holder shall, in any event, be
entitled to sell its Restricted Stock commencing on the 180th day after the
effective date of such registration statement.


                                       4
<PAGE>   5

                  The rights of any holder of Restricted Stock to include its
Restricted Stock in any registration statement filed pursuant to this Section 4
shall terminate as to any shares of Restricted Stock to the extent such shares
become available for resale without restrictions pursuant to Rule 144 under the
Securities Act.

                  5.       Registration Procedures. If and whenever the Company
is required by the provisions of Section 3 or 4 hereof to use its best efforts
to effect the registration of any of the Restricted Stock under the Securities
Act, the Company will, as expeditiously as possible:

                  (a)      prepare (and afford one counsel for the selling
holders reasonable opportunity to review and comment thereon) and file with the
Commission a registration statement (which, in the case of an underwritten
public offering pursuant to Section 3 hereof, shall be on Form S-1 or another
form of general applicability satisfactory to the managing underwriter selected
as therein provided) with respect to such securities and use its best efforts to
cause such registration statement to become and remain effective for the period
of the distribution contemplated thereby (determined as hereinafter provided);

                  (b)      prepare (and afford one counsel for the selling
holders reasonable opportunity to review and comment thereon) and file with the
Commission such amendments and supplements to such registration statement and
the prospectus used in connection therewith as may be necessary to keep such
registration statement effective for the period specified in paragraph (a) above
and as comply with the provisions of the Securities Act with respect to the
disposition of all Restricted Stock covered by such registration statement in
accordance with the sellers' intended method of disposition set forth in such
registration statement for such period;

                  (c)      furnish to each seller and to each underwriter such
number of copies of the registration statement and the prospectus included
therein (including each preliminary prospectus) as such persons may reasonably
request in order to facilitate the public sale or other disposition of the
Restricted Stock covered by such registration statement;

                  (d)      use its best efforts to register or qualify the
Restricted Stock covered by such registration statement under the securities or
blue sky laws of such jurisdictions as the sellers of Restricted Stock or, in
the case of an underwritten public offering, the managing underwriter, shall
reasonably request;

                  (e)      immediately notify each seller under such
registration statement and each underwriter, at any time when a prospectus
relating thereto is required to be delivered under the Securities Act, of the
happening of any event as a result of which the prospectus contained in such
registration statement, as then in effect, includes an untrue statement of a
material fact or omits to state any material fact required to be stated therein
or necessary to make the statements therein not misleading in the light of the
circumstances then existing;

                  (f)      use its best efforts (if the offering is
underwritten) to furnish, at the request of any seller, on the date that
Restricted Stock is delivered to the underwriters for sale pursuant


                                       5
<PAGE>   6

to such registration: (i) an opinion dated such date of counsel representing the
Company for the purposes of such registration, addressed to the underwriters and
to such seller, stating that such registration statement has become effective
under the Securities Act and that (A) to the best knowledge of such counsel, no
stop order suspending the effectiveness thereof has been issued and no
proceedings for that purpose have been instituted or are pending or contemplated
under the Securities Act, (B) the registration statement, the related
prospectus, and each amendment or supplement thereof, comply as to form in all
material respects with the requirements of the Securities Act and the applicable
rules and regulations of the Commission thereunder (except that such counsel
need express no opinion as to financial statements, the notes thereto, and the
financial schedules and other financial and statistical data contained therein)
and (C) to such other effects as may reasonably be requested by counsel for the
underwriters or by such seller or its counsel, and (ii) a letter dated such date
from the independent public accountants retained by the Company, addressed to
the underwriters, stating that they are independent public accountants within
the meaning of the Securities Act and that, in the opinion of such accountants,
the financial statements of the Company included in the registration statement
or the prospectus, or any amendment or supplement thereof, comply as to form in
all material respects with the applicable accounting requirements of the
Securities Act, and such letter shall additionally cover such other financial
matters (including information as to the period ending no more than five
business days prior to the date of such letter) with respect to the registration
in respect of which such letter is being given as such underwriters or seller
may reasonably request; and

                  (g)      make available for inspection by each seller, any
underwriter participating in any distribution pursuant to such registration
statement, and any attorney, accountant or other agent retained by such seller
or underwriter, all financial and other records, pertinent corporate documents
and properties of the Company, and cause the Company's officers, directors and
employees to supply all information reasonably requested by any such seller,
underwriter, attorney, accountant or agent in connection with such registration
statement and permit such seller, attorney, accountant or agent to participate
in the preparation of such registration statement.

For purposes of paragraphs (a) and (b) above and of Section 3(c) hereof, the
period of distribution of Restricted Stock in a firm commitment underwritten
public offering shall be deemed to extend until each underwriter has completed
the distribution of all securities purchased by it, and the period of
distribution of Restricted Stock in any other registration shall be deemed to
extend until the earlier of the sale of all Restricted Stock covered thereby or
six months after the effective date thereof.

                  In connection with each registration hereunder, the selling
holders of Restricted Stock will furnish to the Company in writing such
information with respect to themselves and the proposed distribution by them as
shall be reasonably necessary in order to assure compliance with federal and
applicable state securities laws.

                  In connection with each registration pursuant to Sections 3
and 4 hereof covering an underwritten public offering, the Company agrees to
enter into a written agreement with the


                                       6
<PAGE>   7

managing underwriter selected in the manner herein provided in such form and
containing such provisions as are customary in the securities business for such
an arrangement between major underwriters and companies of the Company's size
and investment stature, provided, however, that such agreement shall not contain
any such provision applicable to the Company which is inconsistent with the
provisions hereof and provided, further, however, that the time and place of he
closing under said agreement shall be as mutually agreed upon among the Company,
such managing underwriter and the selling holders of Restricted Stock.

                  6.       Expenses. All expenses incurred by the Company in
complying with Sections 3 and 4 hereof, including, without limitation, all
registration and filing fees, printing expenses, fees and disbursements of
counsel and independent public accountants for the Company, fees of the National
Association of Securities Dealers, Inc. or any successor thereto, transfer
taxes, fees of transfer agents and registrars, costs of insurance and reasonable
fees and expenses of one counsel for all sellers of Restricted Stock, but
excluding any Selling Expenses, are herein called "Registration Expenses." All
underwriting discounts and selling commissions applicable to the sale of
Restricted Stock are herein called "Selling Expenses."

                  The Company will pay all Registration Expenses in connection
with each registration statement filed pursuant to Section 3 or 4 hereof. All
Selling Expenses in connection with any registration statement filed pursuant to
Section 3 or 4 hereof shall be borne by the participating sellers in proportion
to the number of shares sold by each, or by such persons other than the Company
(except to the extent the Company shall be a seller) as they may agree.

                  7.       Indemnification. In the event of a registration of
any of the Restricted Stock under the Securities Act pursuant to Section 3 or 4
hereof, the Company will indemnify and hold harmless each seller of such
Restricted Stock thereunder and each underwriter of Restricted Stock thereunder
and each other person, if any, who controls such seller or underwriter within
the meaning of the Securities Act, against any losses, claims, damages or
liabilities, joint or several, to which such seller or underwriter or
controlling person may become subject under the Securities Act or otherwise,
insofar as such losses, claims, damages or liabilities (or actions in respect
thereof) arise out of or are based upon any untrue statement or alleged untrue
statement of any material fact contained in any registration statement under
which such Restricted Stock was registered under the Securities Act pursuant to
Section 3 or 4, any preliminary prospectus or final prospectus contained
therein, or any amendment or supplement thereof, or arise out of or are based
upon the omission or alleged omission to state therein a material fact required
to be stated therein or necessary to make the statements therein not misleading,
and will reimburse each such Seller, each such underwriter and each such
controlling person for any legal or other expenses reasonably incurred by them
in connection with investigating or defending any such loss, claim, damage,
liability or action; provided, however, that the Company will not be liable in
any such case if and to the extent that any such loss, claim, damage or
liability arises out of or is based upon an untrue statement or alleged untrue
statement or omission or alleged omission so made in conformity with information
furnished by such seller, such underwriter or such controlling person in writing
specifically for use in such registration statement or prospectus.


                                       7
<PAGE>   8

                  In the event of a registration of any of the Restricted Stock
under the Securities Act pursuant to Section 3 or 4 hereof, each seller of such
Restricted Stock thereunder, severally and not jointly, will indemnify and hold
harmless the Company and each person, if any, who controls the Company within
the meaning of the Securities Act, each officer of the Company who signs the
registration statement, each director of the Company, each underwriter and each
person who controls any underwriter within the meaning of the Securities Act,
against all losses, claims, damages or liabilities, joint or several, to which
the Company or such officer or director or underwriter or controlling person may
become subject under the Securities Act or otherwise, insofar as such losses,
claims, damages or liabilities (or actions in respect thereof) arise out of or
are based upon any untrue statement or alleged untrue statement of any material
fact contained in the registration statement under which such Restricted Stock
was registered under the Securities Act pursuant to Section 3 or 4, any
preliminary prospectus or final prospectus contained therein, or any amendment
or supplement thereof, or arise out of or are based upon the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, and will reimburse the
Company and each such officer, director, underwriter and controlling person for
any legal or other expenses reasonably incurred by them in connection with
investigating or defending any such loss, claim, damage, liability or action;
provided, however, that such seller will be liable hereunder in any such case if
and only to the extent that any such loss, claim, damage or liability arises out
of or is based upon an untrue statement or alleged untrue statement or omission
or alleged omission made in reliance upon and in conformity with information
pertaining to such seller, as such, furnished in writing to the Company by such
seller specifically for use in such registration statement or prospectus;
provided, further, however, that the liability of each seller hereunder shall be
limited to the proportion of any such loss, claim, damage, liability or expense
which is equal to the proportion that the public offering price of shares sold
by such seller under such registration statement bears to the total public
offering price of all securities sold thereunder, but not to exceed the proceeds
(net of underwriting discounts and commissions) received by such seller from the
sale of Restricted Stock covered by such registration statement.

                  Promptly after receipt by an indemnified party hereunder of
notice of the commencement of any action, such indemnified party shall, if a
claim in respect thereof is to be made against the indemnifying party hereunder,
notify the indemnifying party in writing thereof, but the omission so to notify
the indemnifying party shall not relieve it from any liability which it may have
to any indemnified party other than under this Section 7. In case any such
action shall be brought against any indemnified party and it shall notify the
indemnifying party of the commencement thereof, the indemnifying party shall be
entitled to participate in and, to the extent it shall wish, to assume and
undertake the defense thereof with counsel satisfactory to such indemnified
party, and, after notice from the indemnifying party to such indemnified party
of its election so to assume and undertake the defense thereof, the indemnifying
party shall not be liable to such indemnified party under this Section 7 for any
legal expenses subsequently incurred by such indemnified party in connection
with the defense thereof other than reasonable costs of investigation and of
liaison with counsel so selected; provided, however, that, if the defendants in
any such action include both the indemnified party and the indemnifying party
and the interests of the indemnified party reasonably may be deemed to conflict
with the interests of the indemnifying


                                       8
<PAGE>   9

party, the indemnified party shall have the right to select a separate counsel
and to assume such legal defenses and otherwise to participate in the defense of
such action, with the expenses and fees of such separate counsel and other
expenses related to such participation to be reimbursed by the indemnifying
party as incurred.

                  Notwithstanding the foregoing, any indemnified party shall
have the right to retain its own counsel in any such action, but the fees and
disbursements of such counsel shall be at the expense of such indemnified party
unless (i) the indemnifying party shall have failed to retain counsel for such
indemnified party as aforesaid, (ii) the interests of such indemnified party may
be reasonably deemed to conflict with the interests of the indemnifying party as
aforesaid or (iii) the indemnifying party and such indemnified party shall have
mutually agreed to the retention of such counsel. It is understood that the
indemnifying party shall not, in connection with any action or related actions
in the same jurisdiction, be liable for the fees and disbursements of more than
one separate firm qualified in such jurisdiction to act as counsel for the
indemnified party (except to the extent set forth in clause (ii) and (iii) in
the prior sentence of this paragraph). The indemnifying party shall not be
liable for any settlement of any proceeding effected without its written
consent, but if settled with such consent or if there be a final judgment for
the plaintiff, the indemnifying party agrees to indemnify the indemnified party
from and against any loss or liability by reason of such settlement or judgment.

                  If the indemnification provided for in the first two
paragraphs of this Section 7 is unavailable or insufficient to hold harmless an
indemnified party under such paragraphs in respect of any losses, claims,
damages or liabilities or actions in respect thereof referred to therein, then
each indemnifying party shall in lieu of indemnifying such indemnified party
contribute to the amount paid or payable by such indemnified party as a result
of such losses, claims, damages, liabilities or actions in such proportion as
appropriate to reflect the relative fault of the Company, on the one hand, and
the underwriters and the sellers of such Restricted Stock, on the other, in
connection with the statements or omissions which resulted in such losses,
claims, damages, liabilities or actions as well as any other relevant equitable
considerations, including the failure to give any notice under the third
paragraph of this Section 7. The relative fault shall be determined by reference
to, among other things, whether the untrue or alleged untrue statement of a
material fact relates to information supplied by the Company, on the one hand,
or the underwriters and the sellers of such Restricted Stock, on the other, and
to the parties' relative intent, knowledge, access to information and
opportunity to correct or prevent such statement or omission. The Company and
each of you agree that it would not be just and equitable if contributions
pursuant to this paragraph were determined by pro rata allocation (even if all
of the sellers of such Restricted Stock were treated as one entity for such
purpose) or by any other method of allocation which did not take account of the
equitable considerations referred to above in this paragraph. The amount paid or
payable by an indemnified party as a result of the losses, claims, damages,
liabilities or action in respect thereof, referred to above in this paragraph,
shall be deemed to include any legal or other expenses reasonably incurred by
such indemnified party in connection with investigating or defending any such
action or claim. Notwithstanding the provisions of this paragraph, the sellers
of such Restricted Stock shall not be required to contribute any amount in
excess of the amount, if any, by which the total price at which the Common Stock
sold by each of them was


                                       9
<PAGE>   10

offered to the public exceeds the amount of any damages which they would have
otherwise been required to pay by reason of such untrue or alleged untrue
statement or omission. No person guilty of fraudulent misrepresentations (within
the meaning of Section 11(f) of the Securities Act), shall be entitled to
contribution from any person who is not guilty of such fraudulent
misrepresentation.

                  The indemnification of underwriters provided for in this
Section 7 shall be on such other terms and conditions as are at the time
customary and reasonably required by such underwriters. In that event the
indemnification of the sellers of Restricted Stock in such underwriting shall at
the sellers' request be modified to conform to such terms and conditions.

                  8.       Changes in Common Stock. If, and as often as, there
are any changes in the Common Stock by way of stock split, stock dividend,
combination or reclassification, or through merger, consolidation,
reorganization or recapitalization, or by any other means, appropriate
adjustment shall be made in the provisions hereof, as may be required, so that
the rights and privileges granted hereby shall continue with respect to the
Common Stock as so changed.

                  9.       Representations and Warranties of the Company. The
Company represents and warrants to you as follows:

                  (a)      The execution, delivery and performance of this
Agreement by the Company have been duly authorized by all requisite corporate
action and will not violate any provision of law, any order of any court or
other agency of government, the Certificate of Incorporation or By-laws of the
Company, or any provision of any indenture, agreement or other instrument to
which it or any of its properties or assets is bound, or conflict with, result
in a breach of or constitute (with due notice or lapse of time or both) a
default under any such indenture, agreement or other instrument, or result in
the creation or imposition of any lien, charge or encumbrance of any nature
whatsoever upon any of the properties or assets of the Company.

                  (b)      This Agreement has been duly executed and delivered
by the Company and constitutes the legal, valid and binding obligation of the
Company, enforceable in accordance with its terms, subject to considerations of
public policy in the case of the indemnification provisions hereof.

                  10.      Rule 144 Reporting. The Company agrees with you as
follows:

                  (a)      The Company shall make and keep public information
available, as those terms are understood and defined in Rule 144 under the
Securities Act, at all times from and after the date it is first required to do
so.

                  (b)      The Company shall file with the Commission in a
timely manner all reports and other documents as the Commission may prescribe
under Section 13(a) or 15(d) of the


                                       10
<PAGE>   11

Exchange Act at any time after the Company has become subject to such reporting
requirements of the Exchange Act.

                  (c)      The Company shall furnish to such holder of
Restricted Stock forthwith upon request (i) a written statement by the Company
as to its compliance with the reporting requirements of Rule 144 (at any time
from and after the date it first becomes subject to such reporting requirements)
and of the Securities Act and the Exchange Act (at any time after it has become
subject to such reporting requirements), (ii) a copy of the most recent annual
or quarterly report of the Company, and (iii) such other reports and documents
so filed as a holder may reasonably request to avail itself of any rule or
regulation of the Commission allowing a holder of Restricted Stock to sell any
such securities without registration.

                  11.      Miscellaneous.

                  (a)      All covenants and agreements contained in this
Agreement by or on behalf of any of the parties hereto shall bind and inure to
the benefit of the respective successors and assigns of the parties hereto
whether so expressed or not. Without limiting the generality of the foregoing,
the registration rights conferred herein on the holders of Restricted Stock
shall inure to the benefit of any and all subsequent holders from time to time
of the Restricted Stock for so long as the certificates representing the
Restricted Stock shall be required to bear the legend specified in Section 2
hereof.

                  (b)      In the event of a breach by the Company of any of its
obligations under this Agreement, each holder of Restricted Stock, in addition
to being entitled to exercise all rights provided herein or granted by law,
including recovery of damages, will be entitled to specific performance of its
rights under this Agreement. The Company and the other parties hereto agree that
monetary damages would not be adequate compensation for any loss incurred by
reason of a breach of the Company of any of the provisions of this Agreement and
hereby further agree that, in the event of any action for specific performance
in respect of such breach, the Company shall waive the defense that a remedy at
law would be adequate.

                  (c)      All notices, requests, consents and other
communications hereunder shall be in writing, and shall be personally delivered,
or shall be sent by national overnight courier service or by certified or
registered mail, postage prepaid and addressed as follows:

                  if to the Company, to it at:

                  MedCath Holdings, Inc.
                  7621 Little Avenue, Suite 106
                  Charlotte, North Carolina 28226
                  Attention:  Richard J.  Post
                  Facsimile:  704-541-2615

                  with copies to:


                                       11
<PAGE>   12

                  Simpson Thacher & Bartlett
                  425 Lexington Avenue
                  New York, New York 10017-3954
                  Attention:  Gary I. Horowitz
                  Facsimile:  212-455-2502

                  and

                  Reboul, MacMurray, Hewitt, Maynard & Kristol
                  45 Rockefeller Plaza
                  New York, New York 10111
                  Attention:  Karen C. Wiedemann
                  Facsimile:  212-841-5725

                  if to any holder of Restricted Stock, to it at the address set
         forth in Schedule I hereto;

                  if to any subsequent holder of Restricted Stock, to it at such
         address as may have been furnished to the Company in writing by such
         holder;

                  or, in any case, at such other address or addresses as shall
         have been furnished in writing to the Company (in the case of a holder
         of Restricted Stock) or to the holders of Restricted Stock (in the case
         of the Company).

                  (d)      This Agreement shall be governed by and construed in
accordance with the laws of the State of New York applicable to transactions to
be performed in that state.

                  (e)      This Agreement constitutes the entire agreement of
the parties with respect to the subject matter hereof and may not be modified or
amended except in writing signed by the Company and the holders of not less than
two-thirds of the Restricted Stock then outstanding; provided that no such
modification or amendment shall deprive any holder of Restricted Stock of any
material right under this Agreement without such holder's consent. The Company
will not grant any registration rights to any other person without the written
consent of the holders of at least two-thirds of the Restricted Stock then
outstanding if such rights could reasonably be expected to conflict with, or be
on a parity with, the rights of holders of Restricted Stock granted under this
Agreement.

                  (f)      This Agreement may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.


                                       12
<PAGE>   13

                  Please indicate your acceptance of the foregoing by signing
and returning the enclosed counterpart of this letter, whereupon this letter
(herein sometimes called "this Agreement") shall be a binding agreement between
the Company and you.

                                             Very truly yours,

                                             MEDCATH HOLDINGS, INC.



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

AGREED TO AND ACCEPTED
as of the date first
above written:

                                             MEDCATH 1998 LLC

                                             By: KKR 1996 FUND, L.P.,
                                                 a Member

                                             By: KKR Associates 1996, L.P.
                                                 its General Partner

                                             By: KKR 1996 GP LLC
                                                 its General Partner


                                             By:/s/ Edward A. Gilhuly
                                                ---------------------------
                                                Name: Edward A. Gilhuly
                                                Title:  Member
<PAGE>   14

                                             WCAS STOCKHOLDERS:

                                             WELSH, CARSON, ANDERSON
                                              & STOWE VII, L.P.

                                             By: WCAS VII Partners, L.P.
                                             General Partner


                                             By:/s/ Laura VanBuren
                                                ---------------------------
                                             Name:
                                             Title:

                                             WCAS HEALTHCARE PARTNERS, L.P.

                                             By:  WCAS HP Partners
                                             General Partner


                                             By:/s/ Laura VanBuren
                                                ---------------------------
                                             Name:
                                             Title: Attorney in Fact

                                             Patrick J. Welsh
                                             Russell L. Carson
                                             Bruce K. Anderson
                                             Richard H. Stowe
                                             Andrew M. Paul
                                             Thomas E. McInerney
                                             Robert A. Minicucci
                                             Anthony J. deNicola
                                             Paul B. Queally


                                             /s/ Laura VanBuren
                                             -----------------------
                                             By: Laura VanBuren
                                             Attorney-in-Fact
<PAGE>   15

                                             /s/ Lawrence B. Sorrell
                                             -----------------------
                                             Lawrence B. Sorrell


                                             /s/ Rudolph E. Rupert
                                             -----------------------
                                             Rudolph E. Rupert


                                             /s/ D. Scott Mackesy
                                             -----------------------
                                             D. Scott Mackesy


                                             /s/ James T. Kelly
                                             -----------------------
                                             James T. Kelly
<PAGE>   16
                                   SCHEDULE I

1.    MedCath 1998 LLC

c/o Kohlberg Kravis Roberts & Co.
2800 Sand Hill Road, Suite 200
Menlo Park, California 94025
Attention: Edward A. Gilhuly
Facsimile: 650-233-6544

2.    WCAS Stockholders

Welsh, Carson, Andreson
  & Stowe VII, L.P.
WCAS Healthcare
  Partners, L.P.
Patrick J. Welsh
Russell L. Carson
Bruce K. Anderson
Richard H. Stowe
Andrew M. Paul
Thomas E. McInerney
Robert A. Minicucci
Anthony deNicola
Paul B. Queally
Lawrence B. Sorrell
Rudolph E. Rupert
D. Scott Mackesy
James T. Kelly

c/o Welsh, Carson, Anderson
  & Stowe
320 Park Avenue, Suite 2500
New York, NY 10022-9500
Facsimile: 212-893-9575