THE RPTR ON A PRADO 4 SID WAS GIVEN VECTORS THEN TOLD TO INTERCEPT THE PDZ 130 DEG RADIAL AND CONTINUE THE DEP. PRIOR TO INTERCEPTING THE 130 DEG RADIAL ATC SAID TO TURN TO 110 DEGS TO INTERCEPT THE THERMAL TRANSITION SE OF PDZ. THE FREQ WAS SO CONGESTED THEY COULD NOT GET A CLARIFICATION OF WHETHER TO INTERCEPT THE 130 DEG RADIAL OR CONTINUE ON THROUGH TO THE SLI 080 DEG RADIAL. THEY TURNED ON THE 130 DEG RADIAL AND HAD A TCASII RA WITH A SMALL ACFT. THE CTLR INTENDED THEY WOULD CONTINUE TO THE SLI 080 DEG RADIAL.

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WE DEPARTED ONT RWY 26R ON THE PRADO 4 PDZ. AS WE STARTED THE L TURN; WE WERE ASSIGNED A 170 DEG HDG FOR TFC. NOW CLR OF THAT TFC; WE WERE GIVEN A HDG OF 100 DEGS TO INTERCEPT THE PDZ VOR 130 DEG RADIAL AND CONTINUE THE DEP. CLBING THROUGH 6000 FT FOR 7000 FT MSL AN AIRLINER AT 12 O'CLOCK AND 9000 FT WAS CALLED TO OUR ATTN. AFTER WE HAD THE AIRLINER IN SIGHT; WE WERE TOLD TO CLB TO 12000 FT WITH VISUAL REF TO AIRLINER (IT WAS MOVING FROM OUR L TO OUR R). THEN WE WERE TOLD A 'HDG OF 110 DEGS TO INTERCEPT THE THERMAL TRANSITION SE OF PARADISE.' WE WERE NOT SURE IF THIS CTLR INTENDED US TO INTERCEPT 130 DEG RADIAL OFF PDZ OR THE 080 DEG RADIAL OFF SEAL BEACH. RADIO TFC WAS SO HVY THAT WE COULD NOT GET A CLARIFICATION FROM THE CTLR. AS WE BEGAN A SLOW CLB TO 12000 FT WE INTERCEPTED THE 130 DEG RADIAL. ON OUR TCASII SCREEN WE NOTICED TFC AT 8500 FT. WE LEVELED AT 8000 FT AND GOT AN RA. WE THEN SAW THE TFC (A SMALL PVT PLANE). HE ALSO PASSED FROM OUR L TO OUR R. AFTER HE CLRED; WE CONTINUED OUR CLB TO 12000 FT. THE CTLR THEN TOLD US WE WERE TO INTERCEPT THE SEAL BEACH VOR 080 DEG RADIAL (THIS WAS HIS ORIGINAL INTENTION). BY OUR FLYING THE 130 DEG RADIAL; THIS CAUSED OUR CONFLICT WITH THE PVT PLANE. I BELIEVE THE MAIN PROB WAS THE CTLR NOT BEING EXPLICIT ENOUGH WITH US. THE SECOND PROB WAS HIS RADIO FREQ BEING SO CONGESTED THAT WE WERE NOT ABLE TO CLARIFY HIS INTENTION.