NMAC BETWEEN ACR-SMT AND ACR-LGT AFTER TKOF FROM PARALLEL RWYS.

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UPON BEING CLRED FOR TKOF ON RWY 1R SFO; WE WERE ADVISED BY SFO TWR (120.5) THAT SMT WHO HAD JUST BEEN CLRED FOR TKOF ON RWY 1L WOULD MAINTAIN RWY HDG. OUR DEP CLRNC WAS THE SFO 3 WITH AN INITIAL HDG INSTRUCTION OF 030 DEGS FOR VECTORS. JUST AFTER LIFT OFF I OBSERVED SMT TURNING RIGHT TO A HDG WHICH PUT HIS ACFT IN A POS XING OUR DEP PATH AHEAD OF AND SLIGHTLY ABOVE US. I IMMEDIATELY INITIATED A RIGHT TURN STARTING AT APPROX 100' MSL TO KEEP OUR COURSES FROM CONVERGING FURTHER. AFTER GAINING SOME LAT SEP; WE FLEW A PARALLEL COURSE TO SMT QUICKLY OVERTAKING AND OUT CLBING THE SMT. I ESTIMATE OUR CLOSEST POINT OF CONVERGENCE AT 75-100'; SHORTLY AFTER I MADE THE EVASIVE TURN. SFO TWR CLRED US TO BAY DEP (120.9); APPARENTLY UNAWARE UNTIL WE ADVISED THEM SUBSEQUENTLY TO THEIR CALL THAT THERE HAD BEEN A SEP CONFLICT. THEY RESPONDED THAT THEY WOULD CONTACT SMT CONCERNING THE CONFLICT. NOW WELL AHEAD AND ABOVE SMT; AND ON OUR ASSIGNED HDG; WE CONTACTED BAY DEP. DEP ISSUED US A HDG OF 050 DEGS AND REQUESTED WE PHONE BAY TRACON COLLECT WHEN TIME PERMITTED. A SUBSEQUENT CALL AND CONVERSATION WITH BAY TRACON SUPVR PRODUCED THE FOLLOWING INFO. HE STATED HE HAD NOT LISTENED TO THE TAPES; BUT THAT HE UNDERSTOOD SMT; WHO WAS ORIGINALLY ASSIGNED A 030 DEG HDG FOR SAC; HAD BEEN GIVEN RWY HDG BY THE TWR. NONE OF MY CREW HAD HEARD SMT TO CLRNC. HE DID STATE THAT THE TWR HAD RESPONSIBILITY FOR ENSURING THAT ACFT HAD SEP IN VISUAL CONDITIONS; WHICH THEY MOST CERTAINLY HAD NOT DONE IN THIS CASE. HE ASKED IF I INTENDED TO RPT THE EVENT; TO WHICH I REPLIED IN THE AFFIRMATIVE. HE THEN STATED HE WOULD TURN THE MATTER OVER TO FAA FLT STANDARDS; AND THAT HE FOUND NO FAULT WITH OUR PROCS.