AN ACR B737 FLC HAD A CONFLICT WITH A C182 AS THEY WERE CLBING OUT AFTER TKOF. THE CTLR; APPARENTLY; ADMITTED FAULT.

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DEPARTING LAX RWY 25R. AT APPROX 2000 FT MSL WE RECEIVED AN RA FOR A TARGET AT 2-2:30 O'CLOCK POS AND SLIGHTLY ABOVE US. REACTING TO THE RA AND LOOKING TO OUR R FRONT QUADRANT WE OBSERVED A SINGLE ENG CESSNA HEADING STRAIGHT FOR US AND BEHIND. PREVIOUSLY; PASSING 1300 FT MSL; SOCAL HAD CLRED US TO CLB TO 15000 FT. AFTER THE CONFLICT; WE ASKED THE CTLR IF HE WAS AWARE OF THE OTHER ACFT. HE RESPONDED IN THE AFFIRMATIVE AND STATED; 'I THOUGHT YOU WOULD PASS BENEATH HIM.' THIS WAS AN UNSAFE SIT AND SHOULD BE BRIEFED TO ALL SOCAL CTLRS. SUPPLEMENTAL INFO FROM ACN 403931: CLRED FOR TKOF RWY 25R TO MAINTAIN 2000 FT AND MAINTAINING VISUAL WITH DEPARTING SAAB AHEAD. UPON CHECKING WITH SOCAL; CLRED TO 15000 FT. CAPT (PF) QUERIED SOCAL IF HE WAS WORKING SMALL ACFT; IF HE WAS AUTHORIZED TO BE THERE; AND IF HE WAS ON RADAR. ALL AFFIRMATIVE. THIS WAS A PARTICULARLY DANGEROUS SIT IN THAT WE WERE ALREADY DISTR WATCHING DEPARTING ACFT AHEAD. WE WERE ON A CHARTED DEP WITH A TURN AT SMO 160 DEG R. I BELIEVE THE VFR CORRIDOR OVER SHORELINE PLACES ALL IN TOO MUCH RISK. ALSO WOULD BE GREAT AID IF FUTURE TCASII CALLED OUT MORE SPECIFIC TFC INFO; IE; TFC 2:00 O'CLOCK POS.