B727 ACFT ON DEP SID AND VECTOR RECEIVED TCASII RA AND AVOIDED B747 CLBING THROUGH THEIR ALT.

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TOOK OFF FROM LGA AT XA45L OFF RWY 13; LGA 8 DEP; WHITESTONE CLB. THE ORIGINAL (FIRST) DEP CTLR ON 120.4 MHZ EVENTUALLY PUT OUR ACFT ON A 250 DEG HDG; CLBING US TO 10000 FT; JUST W OF LGA. APCHING LEVELOFF AT 10000 FT; 2 TARGETS APPEARED ON OUR TCASII DISPLAY AT OUR 11 - 12 O'CLOCK POS; SOMEWHERE AROUND 10-15 MI DISTANT. THE 2 TARGETS WERE VERY CLOSE TO EACH OTHER. ONE TARGET WAS ABOVE OUR ALT; THE OTHER WAS BELOW OUR ALT. ONE TARGET APPEARED LARGE; AND WE GUESSED IT WAS AN ACR. THE OTHER TARGET WE DID NOT SEE AFTER MANY ATTEMPTS TO LOCATE IT. WE DISCUSSED WHETHER THE VISIBLE TARGET WAS THE ONE ABOVE US OR BELOW US; AS WE COULD NOT DETERMINE ITS RELATIVE ALT TO US. WE COULD ALSO NOT DECIDE IF IT WAS MOVING TOWARD OR AWAY FROM US; BUT WE KNEW FROM ITS SILHOUETTE ITS FLT PATH WAS CLOSE TO PARALLEL WITH OURS. AS PER THE LGA 8 SID; WE DID NOT EXCEED 250 KTS BECAUSE OF OUR ALT (LGA 8 SID REQUIRES 250 KT MAX UNTIL LEAVING 11000 FT). OUR ACFT WAS THEN CLRED BY DEP CTL TO CLB TO AND MAINTAIN 11000 FT. BY NOW; IT APPEARED THAT THE 12 O'CLOCK VISIBLE TARGET WAS CLOSE TO OUR ALT. SINCE WE WERE ABOVE THE CLASS B AIRSPACE; WE WERE CONCERNED THAT IT COULD BE A VFR ACFT; OR AN ACFT NOT BEING WORKED BY DEP CTL. WE RPTED LEAVING 10000 FT AND STARTED AN INTENTIONALLY SLOW CLB AT 500 FPM TO EVALUATE THE SEPARATION. AS WE HAD A SEE AND AVOID RESPONSIBILITY; IFR OR VFR; PASSING THROUGH APPROX 10500 FT; WE RECEIVED A TCASII RA TO CLB 1500 FPM; WHICH WE DID; AND SIMULTANEOUSLY RECEIVED THE INSTRUCTION FROM ATC; 'NO DELAY IN YOUR CLB TO 11000 FT; TFC 12 O'CLOCK AND 'X' MI (DON'T RECALL THE NUMBER) CLBING TO 10000 FT.' AT NO TIME BEFORE THIS ADVISORY WERE WE ADVISED OF ANY TFC. WE WERE NEVER TOLD PRIOR TO THIS TIME TO EXPEDITE CLB. I SUSPECT THE TARGET IN QUESTION; WHICH TURNED OUT TO BE A B747; WAS FMS EQUIPPED AND WAS CLBING IN EXCESS OF THE AIM RECOMMENDED RATE OF 500-1500 FPM FOR THE LAST 1000 FT OF CLB. WE INTENTIONALLY CLBED AT 500 FPM FROM 10000 FT TO 11000 FT; UNTIL THE TCASII RA; BECAUSE IT APPEARED THE SAFEST COURSE OF ACTION; NOT KNOWING IF THE TARGET WE SAW WAS ABOVE OR BELOW US. HAD WE BEEN INFORMED OF THE POTENTIAL CONFLICT IN ANY MANNER; IN A TIMELY FASHION; OR BEEN INSTRUCTED TO EXPEDITE CLB; THE LOSS OF SEPARATION (AS TOLD TO ME BY THE TRACON BY PHONE ON THE GND) WOULD NOT HAVE OCCURRED. AS WE PASSED THE B747; WE NOTED ON OUR TCASII A VERT SEPARATION OF 900 FT. WE HAD THE B747 IN SIGHT CONTINUOUSLY; AND MAINTAINED A VISUAL SEPARATION FROM IT; AS TFC HAD NOT BEEN ISSUED TO US BY DEP CTL; NOR WERE WE INFORMED OF ANY POTENTIAL CONFLICT UNTIL INSTRUCTED 'NO DELAY IN YOUR CLB TO 11000 FT.'