ACR RWY 1L DEP FROM SFO DESCRIBED CONFLICT EVENT WHEN RWY 28L ARR CROSSED INTXN; ELECTED TO CONTINUE TKOF; OPERROR RECORDED.

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NORMAL TAXI OUT. APCHING THE RWY 1'S; TWR ASKED IF WE COULD ACCEPT RWY 1L. WE RESPONDED WE PROBABLY COULD; RAN THE NUMBERS; DETERMINED WE HAD THE PERFORMANCE AND REPROGRAMMED THE FMGC. WE THEN WERE CLRED ONTO RWY 1L POS AND HOLD. ONCE IN POS; I CHKED WITH THE FO TO MAKE SURE HE WAS CAUGHT UP AND WE WERE INDEED READY -- THAT WAS AFFIRMATIVE. I RECHKED THE PERFORMANCE DATA; FLAP POS; AND HDG/ALT ON THE FCU. ALL CORRECT. I LOOKED UP TO SEE ANOTHER CARRIER SLOWLY ROLLING THROUGH THE INTXN ON RWY 28. AS THEY FINALLY CLRED; TWR GAVE US 'CLRED FOR TKOF;' I TURNED ON THE APPROPRIATE LIGHTS; TURNED OFF THE BRAKE AND PUSHED UP THE PWR. THE PWR LEVERS CLICKED INTO THE TOGA DETENT. I VERIFIED THE EPR; AND ANNOUNCED THE FMA'S. AS I FOCUSED DOWN THE END OF RWY 1L; I SAW ACFT Y NOSE COME INTO VIEW. I DETERMINED HE WOULD CLR RWY 1L IN A COUPLE SECONDS. I HEARD TWR ON THE RADIO 'OH (SOMETHING) -- ACFT X.' I RESPONDED; 'WE HAVE Y' AND CONTINUED THE ROLL. I ESTIMATE THAT ACFT Y CLRED RWY 1L AS WE ACCELERATED THROUGH 60 KTS; AND DETERMINED CONTINUING THE TKOF AS THE SAFEST COURSE OF ACTION. WE PROBABLY DIDN'T GET ANY CLOSER THAN 3000 FT BEFORE HE VACATED.