NMAC AND TCASII DURING TKOF.

Narrative

MY ACFT FLT X CLRED FOR TKOF ON RWY 36R AT DFW. AT ABOUT 700 AGL; TWR GAVE FLT X A HDG OF 350 DEGS. SIMULTANEOUSLY; FLT X RECEIVED TCASII WARNING TO 'REDUCE CLB.' ABOUT 800-1000 FT AGL; FLT Y CAME DIRECTLY ABEAM THE COCKPIT L SIDE; CO-ALT; WITH ABOUT 150 FT HORIZ SEPARATION: AGAIN; TWR CTLR ISSUED INSTRUCTIONS TO FLY HDG OF 350 DEGS FOR FLT X. I DID NOT COMPLY WITH TWR'S INSTRUCTIONS AS THIS WOULD HAVE REDUCED SEPARATION WITH FLT Y ABOUT 1000-1200 FT AGL; FLT Y BEGAN A L BANK TURN AND BEGAN TO INCREASE HORIZ SEPARATION. ANALYSIS: FLT Y WAS EXECUTING A GAR FROM RWY 36L AT THE TIME OF THE INCIDENT BECAUSE OF AN ACFT ON THE RWY. TWR CTLR; (IN MY VIEW) CAUSED THE SIT TO OCCUR FOR FOLLOWING REASONS: 1) TOO LITTLE SEPARATION BTWN ACFT LNDG ON RWY 36L LED TO A NEED FOR FLT Y TO GAR. 2) ONCE FLT Y INITIATED GAR; TWR DID NOT ISSUE INSTRUCTIONS TO INSURE SEPARATION BTWN FLT Y ON THE GO AND FLT X ON TKOF. 3) TWR COMPOUNDED THE PROB BY ISSUING INSTRUCTIONS (L HDG 350 DEG) TO FLT X WHICH WOULD HAVE INCREASED THE CONFLICT. HAD I COMPLIED WITH THOSE INSTRUCTIONS; IT COULD HAVE RESULTED IN A MID-AIR COLLISION.