I have been told that in California, personal injury contingency
lawsuit damages awarded to a victim of a traffic accident are by law
distributed in thirds: one third to the victim, one third to the
attorney, and one third to the doctor who treated the victim. Further,
if the awarded damages are insuficient to fully cover the doctor's
bill, the damages are nonetheless distributed as above, even if that
means that the doctor doesn't get paid in full what he is charging.
Is this true? What statutes apply?

Hello.

What you've been told is not correct.

In personal injury cases, attorneys' contingency fees are not fixed by
California law.  Rather, contingency fees are negotiable by the
attorney and client. An attorney and client could agree to the
one-third split that you described, but they would not be required to
agree to it.

" 10. What is the law on the contingency percentage that lawyer should
charge?
The contingency fee is not set by law but is negotiable between the
attorney and client."
source: familylegalhelp.com
http://www.familylegalhelp.com/resources/personal_injury_law.html


The statutes that apply to contingency fees are California Business &
Profession Code Sections 6146 & 6147.

Section 6146 applies to health care malpractice cases and imposes
limits on the size of contingency fees in those cases.

Section 6147 lays out the requirements for a contingency fee contract
between an attorney and client:

"6147.  (a) An attorney who contracts to represent a client on a
contingency fee basis shall, at the time the contract is entered
into, provide a duplicate copy of the contract, signed by both the
attorney and the client, or the client's guardian or representative,
to the plaintiff, or to the client's guardian or representative.  The
contract shall be in writing and shall include, but is not limited
to, all of the following:
   (1) A statement of the contingency fee rate that the client and
attorney have agreed upon.
   (2) A statement as to how disbursements and costs incurred in
connection with the prosecution or settlement of the claim will
affect the contingency fee and the client's recovery.
   (3) A statement as to what extent, if any, the client could be
required to pay any compensation to the attorney for related matters
that arise out of their relationship not covered by their contingency
fee contract.  This may include any amounts collected for the
plaintiff by the attorney.
   (4) Unless the claim is subject to the provisions of Section 6146,
a statement that the fee is not set by law but is negotiable between
attorney and client.
   (5) If the claim is subject to the provisions of Section 6146, a
statement that the rates set forth in that section are the maximum
limits for the contingency fee agreement, and that the attorney and
client may negotiate a lower rate.
   (b) Failure to comply with any provision of this section renders
the agreement voidable at the option of the plaintiff, and the
attorney shall thereupon be entitled to collect a reasonable fee.
   (c) This section shall not apply to contingency fee contracts for
the recovery of workers' compensation benefits.
   (d) This section shall become operative on January 1, 2000."

source: California Business and Professions Code Section 6146-6147
http://www.leginfo.ca.gov/cgi-bin/calawquery?codesection=bpc&codebody=6147&hits=20


Specifically note subsection (a)(4) above:

"(4) Unless the claim is subject to the provisions of Section 6146,
a statement that the fee is not set by law but is negotiable between
attorney and client."


Also See:
California State Bar
"HOW CAN I FIND AND HIRE THE RIGHT LAWYER?
12. Do all lawyers charge the same kind of fee?"
http://www.calbar.ca.gov/state/calbar/calbar_generic.jsp?sImagePath=Hiring_A_Lawyer.gif&sCategoryPath=/Home/Public%20Services/Consumer%20Information/Pamphlets&sHeading=Hiring%20a%20Lawyer&sFileType=HTML&sCatHtmlPath=html/Pamphlets_Hire-Lawyer.html#lawer12

search strategy: 
"contingency fees", california

I hope this helps.  Also, please note the disclaimer below. Google
Answers is for informational purposes only, and should not be taken as
a substitute for professional legal advice. No warranties are
expressed or implied.

This answer covered what I needed to know and included good links for further study.