DEPING B737 ON INITIAL TKOF CLB FROM TUS RWY 29R IS PASSED BY F-16 ON GAR.

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TUS HAD JUST CHANGED THE ACTIVE RWY FROM 11 TO 29 AND WE WERE THE FIRST OF THREE AIR CARRIERS AT THE END WAITING DEP. TWR FREQ WAS EXTREMELY HEAVY WITH NUMEROUS (AT LEAST FOUR) SMALL GA PLANES TO PARALLEL RWY IN THE PATTERN AND SEVERAL ANG F-16'S WORKING THE PATTERN AS WELL. TWR TOLD US TO POSITION AND HOLD ON 29R; FOLLOWED SHORTLY BY INSTRUCTIONS TO TAXI OFF THE RWY AS APCH WASN'T ACCEPTING DEPARTURES. WE WERE TOLD TO TAKE THE FIRST RIGHT. THE FIRST RIGHT OFF WAS A15; ABOUT 2000 FT FROM THE NUMBERS OF RWY 29R. AS WE APCHED A-15 THE TWR TOLD US WE WERE THEN CLRED FOR TKOF. AS WE HAD JUST PUT 2000 FT OF RWY BEHIND US; I WANTED TO CHECK THE PERFORMANCE AND TOLD THE TWR WE WOULD NEED A FEW SECONDS TO DO THAT. I BELIEVE WE SAID 15 SECS AND WE WANTED TO HOLD OUR POSITION. TWR SAID FINE AND CONTINUED WITH WORKING HIS VFR PATTERN TFC. SATISFIED WITH THE PERFORMANCE; I WANTED TO VERIFY WITH THE TWR WE WERE STILL CLRED FOR TKOF WHICH TOOK SOME TIME TO BREAK IN ON THE FREQ. THE TWR CTLR SAID WE WERE CLRED FOR TKOF AND SAID THERE WAS AN F-16 ON FINAL. WE STARTED DOWN THE RWY AND HEARD NUMEROUS XMISSIONS OVER THE RADIO REGARDING CESSNA'S AND THE LIKE AND ROTATED NORMALLY. AFTER ROTATION (FO'S LEG); I NOTICED A YELLOW TA ON THE TCAS AND ASSUMED IT WAS A GA AIRPLANE ON THE PARALLEL RWY. TWR THEN SAID SOMETHING TO THE EFFECT 'PREVIOUSLY CALLED F-16 TFC NO FACTOR; SWITCH TO DEP'. ABOUT THAT TIME; THE TCAS GAVE 'MONITOR VERTICAL SPEED' AND I NOTICED THE TARGET AT 300 FT BELOW US AND SLIGHTLY TO THE R. AT THAT TIME; WE WERE CLIMBING THROUGH ABOUT 700 FT. NEXT CAME 'CLIMB' AND THE RED ARC ON THE TCAS. THE FO SAID HE SAW THE F-16 BELOW AND ABOUT TWO WING LENGTHS TO THE RIGHT OF US TURNING AWAY. BEFORE SWITCHING TO DEP; I ASKED THE TWR ABOUT THE F-16 AND HE SAID HE CALLED IT. THE FO THEN REMINDED ME; HE SAID THE F-16 WAS ON FINAL. WE THOUGHT HE WAS BEHIND US. AFTER DISCUSSING WHAT HAPPENED WITH THE FO; WE CAME TO THE CONCLUSION THE F-16 HAD COME FROM BEHIND; ACCELERATED AT LOW ALTITUDE. UNTIL BELOW AND AHEAD OF US; AND THEN TURNED RIGHT FOR HIS DOWNWIND. HIS MANEUVER CAUSED OUR TCAS TO GIVE A 'CLIMB' RA EVEN THOUGH WE WERE ALREADY CLIMBING AT MAX RATE FOLLOWING TKOF. WE DID NOT HEAR ANY XMISSIONS FROM THE F-16 AND I DO NOT KNOW IF HE EVEN EVER SAW US. THE TWR CTLR SEEMED VERY DISINTERESTED IN OUR CONCERNS. SUPPLEMENTAL INFO FROM ACN 541579: I NOTICED THE F-16 APPROX 200 FT BELOW US AND APPROX 200 FT TO MY R AND CLIMBING. HE PASSED US AND MADE A CROSSWIND TURN AWAY FROM US. I NEVER HEARD THE TWR CTLR POINT OUT THE TFC AFTER HE INITIALLY TOLD US THE F-16 WAS ON FINAL. THE CAPT QUERIED THE TWR AND THEY RESPONDED HE NOTIFIED US IT WAS NO FACTOR AND GAVE US A SWITCH TO DEPARTURE. TWR WAS VERY BUSY AND COULD EASILY HAVE TOLD THE F-16 TO GO AROUND PRIOR TO OUR TKOF. THIS WOULD HAVE PREVENTED THE PROB. THERE WAS NO REASON FOR THE F-16 TO BE WHERE HE WAS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CAPT ADVISED INCIDENT WAS ELEVATED THROUGH COMPANY TO ITS ATC COORDINATOR. AS OF YET; NO RESPONSE HAS BEEN RECEIVED BY RPTR.