ACR X TCASII TA RA UNAUTHORIZED DSCNT FROM ASSIGNED ALT HAD NMAC WITH ACFT Y. EVASIVE ACTION TAKEN. SEE AND AVOID CONCEPT.

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TKOF OUT OF AUSTIN; TX. INITIAL INSTRUCTIONS WERE TURN R TO 230 DEG FOR VECTORS. ON DEP WE WERE GIVEN HDG 320 DEG FOR TFC. THEN 270 DEG HDG CORRECTION FOR TFC AND LEVEL AT 10000 FT. TURN TO 320 DEG WAS GIVEN AND THEN CHANGED TO HDG 310 DEG FOR TFC. DEP THEN TURNED US OVER TO CTR AND APPROX THE SAME TIME WE SAW; VISUALLY; AN ACFT Y AT 12 O'CLOCK AND A TA WAS GIVEN BY THE TCASII. ACFT Y WAS SLIGHTLY HIGH AND MANEUVERING RAPIDLY. A 180 DEG TURN WITH TIGHT TURNING WAS OBSERVED. A RA WAS GIVEN BY THE TCASII; DSND; AS WE OBSERVED THE ACFT Y IN A WING OVER POS HIGH ANGLE OF BANK AND DSNDING. WE DSNDED AND PASSED BELOW THE CONFLICTING ACFT APPROX 500 FT. WE LEVELED AT 9500 FT AND CLBED BACK TO 10000 FT WHEN CLR. I CHKED IN WITH HOUSTON CTR AND TOLD THEM OF THE EVENT. THEY SAID DEP SHOULDN'T HAND US OFF UNTIL WE WERE CLR OF TFC. THERE SEEMED TO BE CONFUSION ON DEPS INSTRUCTIONS AND RADIO TERMINOLOGY AND FLOW OF INSTRUCTIONS. WE WERE GIVEN HDG CHANGES FOR TFC BUT NEVER SAW THE 'TFC' VISUALLY OR ON TCASII INITIALLY. THEN WHEN WE WERE TURNED OVER TO HOUSTON CTR THE ACFT WE CONFLICTED WITH WAS NEVER CALLED OUT BY DEP.