NMAC OCCURRED WHEN DC10 ON FINAL APCH TO RWY 4L IS GIVEN GAR TO AVOID A B727 ON TKOF ROLL FROM THE SAME RWY. RPTR'S TCASII SHOWED 200 FT ALT SEPARATION DURING CLB WITH TFC ABOVE AND BEHIND FLT. NO INDICATION THAT THE LCL CTLR ISSUED TFC INFO OR THAT CLB TURN INSTRUCTIONS WERE GIVEN TO ENSURE SEPARATION BTWN THE 2 ACFT. VISUAL SEPARATION BY THE LCL CTLR MAY HAVE BEEN APPLIED.

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OUR ACFT WAS CLRED TO POS AND HOLD RWY 4L; DC10 ON 3 MI FINAL. AFTER PREVIOUS LNDG DC10 CLRED THE ACTIVE; WE WERE CLRED TKOF RWY 4L. JUST AFTER STARTING TKOF ROLL; TWR ADVISED TO START ROLL; ACFT ON 2 1/2 MI FINAL. WE REPLIED THAT WE WERE ROLLING. AT APPROX 40-50 KTS; TWR ADVISED ACFT BEHIND US TO 'GAR; L SIDE.' AFTER TKOF; R TURN TO 060 DEGS INITIATED AS PER SID PROC. AT ABOUT 600 FT MSL; CAPT NOTED THAT TCASII INDICATED VERY LITTLE LATERAL SEPARATION WITH GAR ACFT; AND TO REDUCE CLB RATE. WE TEMPORARILY LEVELED AT 900 FT; WITH TCASII SHOWING 200 FT VERT SEPARATION. OUR TCASII IS INHIBITED FROM DISPLAYING RA OR AUDIO WARNINGS BELOW 1100 FT AGL; SO NO WARNINGS WERE RECEIVED. AT NO TIME DID WE HAVE VISUAL CONTACT WITH GAR ACFT; AS IT WAS BEHIND AND ABOVE US; AND AS SUCH WE DID NOT KNOW ITS EXACT POS. IF TWR HAD ADVISED US; OR IF THE GAR ACFT CALLED US IN SIGHT; WE WOULD HAVE BEEN MUCH MORE COMFORTABLE ABOUT SEPARATION. OUR HDG OF 060 DEGS AFTER TKOF SHOULD HAVE PROVIDED ADEQUATE COURSE DIVERGENCE IF THE GAR ACFT REMAINED L OF RWY 4L CTRLINE; BUT TCASII DISPLAY DOES NOT PROVIDE SUFFICIENT RESOLUTION AT THESE VERY SMALL RANGES; AND WITHOUT INFO FROM THE TWR TO THE CONTRARY; WE WERE UNSURE OF DISTANCE FROM GAR ACFT. SUPPLEMENTAL INFO FROM ACN 371725: AFTER LIFTOFF/GEAR RETRACTION; I NOTICED AN ACFT SIGNAL ON OUR TCASII DIRECTLY ABOVE AND SLIGHTLY BEHIND US. BEGAN TO IMMEDIATELY LEVEL OFF OUR ACFT SO AS NOT TO FLY UP AND INTO ACFT ABOVE US. THE DEP SID HAD US BEGIN R TURN TO 060 DEGS AT WHICH TIME OUR PATHS BEGAN TO DIVERGE.