SF34 PLT CONCERNED WITH MISSED TFC ALERT OF A TRANSITING VFR T38 FROM ZFW TO D10 APCH. PLT COMMENTS ON OVERALL PROBS INCURRED TRANSITING SPS MILFAC ENRTE TO DFW.

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ON THIS FLT JUST AFTER BEING HANDED OFF TO THE NEXT CTLR AND 5 NM SE OF UKW AT 7000 FT ASSIGNED; WE VISUALLY SPOTTED A T38 IN CLOSE PROX AND VERY CLOSE TO ALT; WITHIN 300 FT; AND CLOSING RAPIDLY. WE MAINTAINED VISUAL SEPARATION AND A FEW SECONDS LATER [RECEIVED A TCASII RA;] WHICH WE RESPONDED TO. WE ADVISED ATC OF THE SIT AND RECEIVED ONLY INFO THAT THE T38 WAS VFR AT 6500 FT; WE WERE SWITCHING FROM 120.75 TO 119.87 AT THE TIME AND IT WAS VFR CONDITIONS AT THE TIME. THIS AREA TO ME SEEMS VERY PROBLEMATIC; AS 3 FACILITIES JOIN IN A CLOSE AREA. THESE BEING ZFW; REGIONAL APCH AND SHEPARD APCH. THE LAPSES OF SHEPARD AFB APCH ARE ALMOST EXPECTED AS CLOSE ENCOUNTERS HAPPEN REGULARLY THERE; BUT I WOULD; UNDER THE CIRCUMSTANCES AND CONSIDERING WE ARE IFR; HAVE EXPECTED FROM BOTH; ZFW AND REGIONAL APCH; A TA. I WOULD ALSO LIKE TO REMIND SOMEONE ON THE ABILITY OF THE CTLRS AT SHEPPARD AFB. PROCS ARE QUESTIONABLE. WE DID RECEIVE AND RESPONDED TO AN RA IN THIS EVENT ALTHOUGH WE DID SPOT THE T38 FIRST. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THOUGH CONCERNED WITH THE LACK OF A TA DURING THE CHANGE FROM ZFW TO D10; THE RPTR DIRECTED COMMENTS TO SHEPPARD AFB (SPS) CTLRS. THE RPTR TRANSITS SPS WEEKLY. THE RPTR STATED THAT HE IS AWARE THAT SPS IS A CTLR TRAINING FACILITY; BUT IS STILL CONCERNED BY THE LACK OF TFC INFO IN A TIMELY MANNER; 'ERRATIC' RADAR VECTORING TO THE FINAL APCH COURSE; AND THE 'UNNECESSARY VECTORING' WHEN ANOTHER APCH TO A DIFFERENT RWY IS REQUESTED.