RPTED LOSS OF SEPARATION BTWN RPTR'S B737 LEVEL AT 10000 FT AND A SECOND B737 AT AN ALT 500 FT TO 700 FT HIGHER.

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AFTER TKOF WE TURNED R TO 210 DEG HDG IN COMPLIANCE WITH THE SID; CLBED AND LEVELED OFF AT 6000 FT. WE WERE THEN ASSIGNED A HDG OF 260 DEGS AND TOLD TO CLB TO 12000 FT BUT WERE HASTILY REASSIGNED AN ALT OF 8000 FT BY ANOTHER CTLR (SUPVR?). AS WITH PREVIOUS DEPS FROM BURBANK ARPT THE DAY PRIOR; WE RECEIVED NUMEROUS HEADINGS; ALTS; AND FREQ CHANGES AS WE WERE CTLED NW OF BURBANK ARPT. AS WE WERE FLYING ON AN ASSIGNED HEADING (300 DEGS; I BELIEVE) AND AT 10000 FT; WE WERE GIVEN ANOTHER FREQ. DUE TO RADIO CONGESTION ON THE NEW FREQ; IT TOOK SEVERAL ATTEMPTS TO CHK IN. DURING THIS TIME; I NOTED A B737-300 FLYING PARALLEL TO OUR DIRECTION OF FLT; LEVEL ABOVE OUR POS APPROX 500-700 FT AND LATERALLY OFFSET BY 800-1000 FT. WHEN I WAS ABLE TO CHK ON FREQ I IMMEDIATELY ADDED THAT I 'HAD THE TFC IN SIGHT.' THE CTLR ASKED IF WE WERE DIRECT TO SXC (I BELIEVE) AND I RESPONDED THAT WE WERE ON AN ASSIGNED HEADING. THE CTLR TURNED US W; THEN S AND ON OUR WAY DIRECT SHOTS/W-291. WE WERE NOT AWARE OF ANY POTENTIAL VIOLATION UNTIL WE WERE ON DSCNT TO ONT AND GIVEN A ZLA PHONE NUMBER TO CALL. I BELIEVE THE FACTORS CONTRIBUTING/RESULTING TO THE LOSS OF SEPARATION WERE: 1) MULTIPLE HEADING AND ALT ASSIGNMENTS; AND FREQ CHANGES SHORTLY AFTER TKOF; AND 2) SOCAL DEP CTLR'S LACK OF ASSIGNING A DIRECT FIM ROUTING. THIS IS APPARENTLY WHERE THE CTLR THOUGHT WE WERE GOING PER THE PHONE CONVERSATION TO ZLA AFTER THE INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID THAT THE CAPT HAD TALKED WITH THE CTR SUPVR WHO INDICATED THAT THEY MIGHT BE VIOLATED BUT ALSO INDICATED THAT THE TAPES; CTR AND BUR; HAD TO BE PLAYED. RPTR HAD HEARD NOTHING FURTHER ON THE INCIDENT. RPTR FELT THE INCIDENT WAS A MISCOM BTWN THE APCH AND THE CTR. RPTR SAID THEY DID NOT GET A TCASII ALERT ON THE OTHER B737.