FLC OF AN ACR ACFT MAINTAINED SEPARATION AFTER TKOF BY MONITORING TCASII AND INCREASING THE BANK OF THE TURN.

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THIS LOSS OF NORMAL SEPARATION OCCURRED 2 NM W OF TVC. MY MLG HAD JUST DEPARTED RWY 28 WITH FO FLYING FROM THE R SEAT. THE TCASII TARGET WAS PROBABLY AN SMA SEL WHICH WAS LIKELY ENGAGED IN STUDENT TRAINING. THE FIELD ELEVATION IS ABOUT 600-800 FT; AND THE WX WAS SUNNY WITH HIGH CLOUDS AND GOOD VISIBILITY. THE SMA WAS AHEAD OF US IN THE LINE FOR TKOF; AND I JUDGE IT WAS PROBABLY ENGAGED IN STUDENT TRAINING; BECAUSE ONE PLT CORRECTED THE OTHER IN HIS RESPONSE TO THE TWR'S CLRNC INTO POS TO HOLD. HE REQUESTED PERMISSION TO DEPART N; AND THE TWR INSTRUCTED HIM TO TURN AFTER PASSING THE FIELD BOUNDARY; BECAUSE TFC WAS LNDG ON RWY 18. TWR CLRED THE SMA FOR TKOF; AND THE PLT STATED HE WAS GOING TO DEPART W. WE WERE CLRED INTO POS TO HOLD. WHILE HOLDING WE DISCUSSED THE TKOF PWR SETTING; AND I THINK SOMEONE LANDED ON RWY 18. THEN TWR CLRED US TO TKOF; TURN L ON COURSE; AND MAINTAIN 3000 FT. ABOUT 1300 FT MSL FO BEGAN A SHALLOW L TURN. AT ABOUT 2000 FT I NOTICED THE TCASII TARGET. I URGED FO TO INCREASE THE TURN; AND I MONITORED THE TCASII AND SCANNED FOR TFC AHEAD. FO INCREASED THE BANK TO 30 DEGS AT ABOUT 200 KTS. AT THE CLOSEST POINT THE TFC WAS ABOUT 1 1/2 MI AT OUR SAME ALT. TCASII SHOWED NEITHER A TA NOR AN RA; ALTHOUGH PERHAPS IT SHOULD HAVE. I HAVE EXPERIENCED SEVERAL TCASII ANOMALIES; AND PERHAPS THIS WAS ANOTHER ONE. I ASKED TWR ABOUT TFC; AND HE DENIED THE PRESENCE OF ANY TFC IN OUR VICINITY. HE THEN SAID THE ONLY TFC WAS AN SMA SEL WHO DEPARTED N; BUT ANOTHER VOICE CAME ON THE FREQ AND STATED THEY HAD DEPARTED W. IF IT HAD NOT BEEN FOR TCASII WE WOULD HAVE FLOWN VERY NEAR THE TFC; WHICH I SUPPOSE WAS THE SMA THAT TOOK OFF A SHORT TIME BEFORE US.