BE9L PLT ON FINAL FOUND HIMSELF IN CONFLICT WITH TFC LNDG ON THE PARALLEL.

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MY KING AIR WAS CLRED FOR VISUAL APCH TO RWY 28R AT SFO. AN ALASKA AIRLINE JET WAS BEING CLRED TO RWY 28L. CTLR MISTAKENLY INFORMED JET THAT KING AIR WAS ON APCH TO RWY 28L. THEN CORRECTED HIMSELF AND SAID KING AIR WAS ON APCH TO RWY 28R. CTLR ASKED ME IF I HAD SIGHTED THE JET AT MY 9 O'CLOCK POS AND 3000 FT MSL. I SAID 'NEGATIVE.' AS IT TURNS OUT; MY L WING WAS PROBABLY IN THE WAY. I THINK THE JET MAY HAVE GOTTEN CONFUSED AND THOUGHT I WAS FOR RWY 28L OR PERHAPS HE WAS SUPPOSED TO BE ON APCH TO RWY 28R. REGARDLESS; HE DID NOT SEE ME EITHER. WITH NEITHER OF US SEEING EACH OTHER; AND PERHAPS THE JET BEING HEADED FOR THE WRONG RWY; THE CTLR'S VOICE OBVIOUSLY INDICATED ALARM AT WHICH I BELIEVE WAS A LOSS OF SEPARATION. HE CANCELED MY APCH CLRNC. I WAS; AT THE TIME; TRYING TO SPOT THE JET SO THAT I COULD EVADE AS REQUIRED. I; THEREFORE; DID NOT INSTANTANEOUSLY RESPOND; CAUSING HIM TO REPEAT THE CANCELLATION -- OBVIOUSLY A MISTAKE ON MY PART. HE HAD ME FLY A 285 DEG HDG AND DSND TO 2000 FT MSL. WHEN ALMOST ABEAM THE RWY 28R OFFSET TO THE R; HE SUDDENLY HANDED ME TO THE TWR WHO CLRED ME TO LAND. I HAD TO CHOP THE PWR; DIVE FOR THE RWY; WHILE THE TWR ASKED ME TO MAINTAIN 180 KTS. MY TURN TO FINAL WAS BASICALLY OVER THE RWY. LNDG WAS UNEVENTFUL AFTER THAT.