AFTER TKOF MIA; A B757 CREW RECEIVED A TCASII TA ON TFC AT 11 O'CLOCK POS AND 2 MI; APPROX 600-800 FT. TFC UNKNOWN TO ATC.

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ATC FACILITY: MIA TWR. LOCATION: MIA. WE WERE CLRED INTO POS AND HOLD ON RWY 9L. AS I STARTED MY TAXI INTO POS; WE GOT THE CLRNC TO TAKE OFF. I ALIGNED THE ACFT WITH THE CTRLINE AND SET TKOF PWR. I ROTATED/LIFTED OFF ON SPD TO A MAX PITCH OF 20 DEGS. SHORTLY AFTER LIFTOFF (THE 300-400 FT); WE HAD A TA. I LOOKED AT THE TCASII 5 MI RANGE AND SAW A TFC AT 11 O'CLOCK POS GOING W TO SW LESS THAN 2 MI AND 200 FT ABOVE. I REDUCED THE PWR SLIGHTLY AND LOWERED THE NOSE. THE TFC PASSED BEHIND US; SAME ALT OR SLIGHTLY BELOW US; LESS THAN 1 MI BEHIND US. WE WERE ASSIGNED A NEW HDG. THE FO PROMPTED THE TWR FOR A FREQ CHANGE. I ASKED THE TWR IF HE WAS AWARE OF THE TFC THAT CAME CLOSE. HE TOLD NO TFC WAS OBSERVED AND THAT DEP WAS LOOKING FOR US. WE CHANGED TO DEP FREQ; AND WERE ADVISED TO MAKE A L TURN FOR TFC. WE COMPLIED; HOWEVER; I REDUCED THE RATE OF TURN TO AVOID A TWRING CLOUD IN OUR PATH. BOTH THE TWR AND DEP DID NOT OBSERVE THE TFC AND ADVISED THAT THERE WAS NO CONFLICT OBSERVED. WHAT LED TO THE TFC CONFLICT; IN MY JUDGEMENT; IS OUR LIGHT TKOF WT AND THE HIGH PERFORMANCE OF B757. WE WERE AIRBORNE AT NO TIME AND PROBABLY WERE ABOVE THE PROFILE; A STANDARD TO PROFILE.