NMAC AT PIT BTWN DEPARTING B737 AND UNKNOWN TFC AT DEP END OF TKOF RWY.

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CLRED INTO POS AND HOLD RWY 28L AT INTXN P BY PIT TWR FOR DEPARTING TFC ON RWY 28R TURNING S. WE WERE SUBSEQUENTLY CLRED FOR TKOF; MAINTAIN RWY HDG; AT 1000 FT AGL (OUR NORMAL PWR REDUCTION/FLAP CONFIGN CHANGE ALT). WE RECEIVED A TCASII RA WITH AN INCREASE CLB VERBAL COMMAND AND RED THROUGHOUT THE UVI IN EXCESS OF 4500 FPM. CHKING OUR TCASII DISPLAY WE NOTED A TARGET JUST OFF OUR L WING AND 200 FT VERT SEPARATION. NO VISUAL CONTACT WAS EVER ESTABLISHED. PIT TWR NEVER ALERTED US TO THE TFC PRIOR TO TKOF OR DURING CLBOUT. THE FIRST TIME THEY TRIED TO SEND US TO DEP I RESPONDED WITH 'STAND BY.' THIS PROMPTED A REPLY FROM PIT TWR SOMETHING TO THE EFFECT 'YOU'VE GOT A VFR...HE GOT YOU IN SIGHT/OR HE GOT YOU VISUAL.' IT HAD BEEN A MAX THRUST TKOF. NO DERATE/STANDARD TEMP AND AIRSPD WAS APPROX V2 +10 KTS. THIS WAS NOT THE TFC THAT HAD DEPARTED RWY 28R. THIS EVENT WAS OVER IN SECONDS AND THE ONLY POSSIBLE RESPONSE TO OUR CONTINUED CLB WOULD HAVE BEEN FIREWALL THRUST AND INCREASE PITCH EVEN HIGHER. I LEARNED ALSO THAT A TCASII RA CAN EXCEED THE PERFORMANCE CAPABILITIES OF THE ACFT. ALL THIS AT THE CORE OF (A TCA) CLASS B AIRSPACE. I'D LOVE TO KNOW WHAT HAPPENED. SUPPLEMENTAL INFO FROM ACN 478961: PIT TWR TOLD US THAT TFC OFF OUR L HAD US IN SIGHT. TWR NEVER GAVE US THIS TFC PRIOR TO TKOF. IT WAS NOT THE TFC THAT HAD DEPARTED RWY 28R PRIOR TO OUR DEP. NEVER ACQUIRED THIS TFC VISUALLY AND TWR NEVER TOLD US WHAT TYPE; DIRECTION OR ALT OF TFC. WE NEVER RESPONDED TO THE RA SINCE IT WAS OVER IN A FEW SECONDS AND WE WERE CLRED TO DEP FREQ.