DEPS FROM CLOSELY SPACED RWYS RESULT IN TCASII RA WHEN ONE ACFT OVERTAKES ANOTHER AT SEA; WA.

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WE WERE INITIALLY CLRED TO CROSS RWY 34R AND HOLD SHORT OF RWY 34L. IN THE PROCESS OF XING; WE WERE CLRED TO TAKE OFF ON RWY 34L. UPON TURNING ONTO THE RWY; THE CAPT TURNED THE ACFT OVER TO ME FOR TKOF. APPARENTLY; AFTER OUR CLRNC FOR TKOF; AN F28 WAS CLRED FOR TKOF FROM THE PARALLEL RWY 34R. I DO NOT KNOW IF THE OTHER ACFT WAS TOLD TO MAINTAIN VISUAL SEPARATION; AS I MISSED HEARING THEIR CLRNC. THE FIRST I KNEW OF THEIR DEP WAS AS THEY PULLED INTO MY PERIPHERAL VIEW JUST PRIOR TO ROTATION. AS SEATTLE DOESN'T DO SIMULTANEOUS DEPS; I WAS SURPRISED TO SEE THEM NEXT TO US. OUR CLRNC WAS THE SEATTLE 2 SID; WHICH TRACKS BASICALLY STRAIGHT OUT THE SEA 338 DEG RADIAL. I BELIEVE THE F28 MUST HAVE BEEN LIGHT AND WAS ABLE TO OUR-ACCELERATE US SO THAT WE ROTATED AT THE SAME TIME. WE WERE NOT SLOW IN EXECUTING OUR TKOF CLRNC. AT LIFTOFF; NEITHER THE CAPT NOR I KNEW IF THE OTHER ACFT HAD BEEN ASSIGNED A TURN OR WAS ON THE SAME SID WE WERE ON. WE DECIDED TO OFFSET OUR COURSE TO THE L UNTIL THE OTHER ACFT'S INTENTIONS WERE CLR. PASSING THROUGH 1100 FT; WE RECEIVE THE FIRST OF 4 RA'S TO DSND; WHICH WE COMPLIED WITH. IT WAS NEVER NECESSARY TO ACTUALLY DSND; AS JUST LEVELING OFF RESULTED IN A 'CLR OF CONFLICT' MESSAGE. WE HAD BEEN SWITCHED TO DEP PRIOR TO THE RA'S WITH NO COM TO OR FROM THE TWR REGARDING THE OTHER ACFT THAT I REMEMBER; THOUGH MY CAPT THOUGHT THE TWR OFFHANDEDLY MENTIONED THE TFC BESIDE US. UPON SWITCHING TO DEP; WE ASKED FOR A L TURN AND ADVISED THEM OF THE RA'S WE WERE RECEIVING. HE GAVE US A 15 DEG L TURN AND MENTIONED OUR PARALLEL TFC WAS A DASH 8 (WHICH IT WAS NOT). AFTER THE TURN; NO FURTHER RA'S RESULTED. I BELIEVE THE TWR MEANT FOR THE F28 TO FOLLOW US AND MAINTAIN VISUAL SEPARATION BUT GAVE THE F28 TKOF CLRNC BEFORE WE WERE ACTUALLY ROLLING. THE ONLY OTHER POSSIBILITY THAT COMES TO MIND IS THAT THEY FORGOT WE WERE THERE AND SINCE I CAN'T REMEMBER THE VERBIAGE IN THEIR CLRNC; I DON'T KNOW WHICH IS CORRECT. I THINK ATC IS UNDER PRESSURE TO MOVE SO MANY AIRPLANES; THAT GIVING A TKOF CLRNC WITH A 'MAINTAIN VISUAL SEPARATION' CAVEAT BEFORE THE FIRST ACFT HAS LIFTED OFF IS ACCEPTED PRACTICE; DESPITE POSSIBLE HAZARDS (SUCH AS WAKE TURB). IN THIS CASE; IT WOULD HAVE BEEN HELPFUL TO KNOW IF ADVANCE THEY WOULD BE PERFORMING CLOSELY SPACED OF SIMULTANEOUS DEPS. WE COULD HAVE SELECTED 'TA ONLY' ON THE TCASII. AND WITH CLOSELY SPACED DEPS; I THINK DEP ACFT SHOULD BE GIVEN DIVERGING HDGS AS IS DONE AT SFO. IF THAT WERE THE CASE; NO CONFLICT (AND THEREFORE NO RA'S) WOULD HAVE RESULTED IN THIS SIT.