B757 CAPT COMPLAINS THAT IFR SEPARATION LOST AFTER DEP CTLR PROVIDES TA OF AN ATR72 AND CLRED RPTR TO CLB AND MAINTAIN VISUAL SEPARATION WITH THE OTHER ACFT WHO HAD RPTR IN SIGHT.

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IN VMC. DEP CTLR PROVIDES TA OF AN ACFT AT OUR 10 O'CLOCK POS. ASKED IF WE HAD ACFT IN SIGHT. WE RESPONDED THAT WE DID. DEP CTLR CLRED US WITH 'MAINTAIN VISUAL SEPARATION ON THAT ACFT; CLB TO 10000 FT. TFC HAS YOU IN SIGHT.' WE WERE AT 8000 FT MSL. I ESTIMATED THAT TFC WAS INITIALLY ABOUT 5 NM. I MISTAKENLY THOUGHT WE WERE ABOUT PARALLEL. I BEGAN A CLB AT ABOUT 1000 FPM; ON AUTOPLT. I THEN SAW THAT I WAS ON INTERCEPT COURSE WITH TFC. IN ORDER TO OBTAIN GREATER VERT SEPARATION; I INCREASED CLB RATE TO 2500 FPM. ALMOST IMMEDIATELY I FELT THAT WE WERE NOT GOING TO HAVE ADEQUATE VERT AND HORIZ SEPARATION. I DISCONNECTED AUTOPLT AND BEGAN STEEP CLB TO GET VERT SEPARATION. WE GOT RA ON TCASII ABOUT THIS TIME TELLING US TO DSND. WE WERE ABOUT 8600 MSL AND TFC WAS AT 9000 FT MSL. I CONTINUED TO CLB SINCE I WAS ALREADY IN A STEEP CLB AND I COULD OBTAIN VERT SEPARATION FASTER IN A CLB THAN IF I PUSHED THE ACFT OVER TO DSND. I ESTIMATE THAT THE ACR PASSED BELOW US JUST AS WE WERE LEVELING AT 10000 FT. THE OTHER ACFT WAS BEHIND US AT THIS POINT.