SMA CLBING ON AN IFR FLT PLAN WAS GIVEN TA TWICE ON A VFR TRINIDAD OVERTAKING FROM BEHIND. ARTCC CTLR ALSO GAVE TA TO THE TRINIDAD. NEITHER ACFT SAW THE OTHER UNTIL THE TRINIDAD PASSED OVERHEAD THE SMA. RPTR UPSET THAT ATC DID NOT GIVE ANY TURNS TO EITHER ACFT FOR AVOIDANCE.

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MY STUDENT AND I WERE ON AN IFR FLT PLAN FROM PRC-LLB. AT 6500 FT MSL OVER DRK; ZAB HAD RADAR CONTACT ON ME. WHEN I WAS OUTBOUND ON THE DRK 259 DEG RADIAL AT ABOUT 4 DME; ZAB ADVISED ME OF TFC (A TRINIDAD) AT 6 O'CLOCK; 2 MI; 8500 FT AND OVERTAKING. I CONTINUED MY CLB THROUGH 8000 FT FOR 10000 FT. THE TRINIDAD WAS VFR ALSO. BOTH THE TRINIDAD AND I RPTED NEGATIVE TFC. A FEW MINS LATER; ZAB RPTED THE TFC TO ME AT 6 O'CLOCK; 1/2 MI; 8500 FT; AND OVERTAKING. I RPTED NEGATIVE TFC AND TOLD ZAB THAT I WOULD NOT BE ABLE TO SEE THE TRINIDAD BECAUSE HE WAS DIRECTLY BEHIND ME. ZAB SIMPLY RESPONDED 'ROGER.' THE TRINIDAD WAS ADVISED OF MY POS AND REPLIED NEGATIVE TFC. A FEW SECONDS LATER; I SAW THE TRINIDAD PASS DIRECTLY OVER THE TOP OF ME FROM MY 7 O'CLOCK TO 10 O'CLOCK POS WITH NO MORE THAN 100 FT VERT SEPARATION. MY CONCERN IS THAT I WAS ON AN IFR FLT PLAN; RPTED NEGATIVE CONTACT TWICE; AND NEITHER ACFT WAS ISSUED INSTRUCTIONS FROM THE CTLR TO OBTAIN SEPARATION. AFTER THE TRINIDAD PASSED OVER; I CALLED ZAB AND TOLD THEM THE TRINIDAD PASSED OVER ME AT LESS THAN 100 FT AND I WANTED TO 'RPT AN NMAC.' THE CTLR STATED; 'ROGER; I TOLD YOU ABOUT THE TFC BOTH TIMES. YOU CAN FILE THE RPT ON THE GND.' I FEEL THAT CONTRIBUTING FACTORS ARE ATC'S LIMITED RADAR COVERAGE IN THE AREA; THE LARGE AMOUNT OF TRAINING ACFT IN THE AREA OF PRESCOTT AND DRAKE VOR; AND ZAB'S HAZARDOUS ATTITUDE TO NOT WANT TO BE BOTHERED PROVIDING TFC SEPARATION IN THE AREA. I KNOW THIS ATTITUDE EXISTS BECAUSE ON APR/XA/97; 4 DAYS PRIOR TO THIS OCCURRENCE; I WAS ON AN IFR FLT PLAN INBOUND TO DRK ON V12 (SAME AIRWAY) AT APPROX 20 DME. I WAS BEGINNING A DSCNT INTO PRESCOTT (VFR) OUT OF 11000 FT MSL. ZAB ADVISED ME OF TFC AT 12 O'CLOCK; 6 MI; OPPOSITE DIRECTION AND CLBING. NEITHER THE OTHER ACFT NOR I HAD VISUAL CONTACT OF EACH OTHER. WHEN THE CTLR RPTED 3 MI AND STILL ON A COLLISION COURSE; I ASKED FOR A R TURN TO AVOID TFC. THE CTLR TOLD EACH OF US TO TURN R 20 DEGS. WHEN I FINALLY SAW THE ACFT PASS OFF MY L WING; WE WERE AT THE SAME ALT; OPPOSITE DIRECTION; BUT HAD ABOUT 1 MI OF HORIZ SEPARATION. I WAS UPSET THAT I HAD TO ASK FOR THE R TURN. I FEEL ATC NEEDS TO TAKE MORE PRECEDENCE IN ISSUING DIVERSIONS TO ENSURE TFC SEPARATION. IT IS STILL ATC'S JOB TO ENSURE IFR TFC SEPARATION IN VFR CONDITIONS IF THE ACFT CANNOT BE SEEN VISUALLY. I DID FILE AN NMAC RPT WITH PRESCOTT FSS ON APR/XB/97.