INSTRUCTOR TRAINEE INADVERTENTLY MADE AN UNAUTH TKOF.

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I WAS RECEIVING DUAL INSTRUCTION IN A SMA SEL; FOR AN UPCOMING CFI CHECK RIDE. WE RECEIVED TAXI CLRNC 'TO RWY 19R; HOLD SHORT OF RWY 19L.' AS WE TAXIED NBOUND ON ALPHA ON THE E SIDE OF THE FIELD; MY INSTRUCTOR AND I WERE DISCUSSING THE LESSON FOR THE DAY. WE TURNED ONTO TXWY C WHICH PARALLELS ALPHA. WHEN WE WERE APPROX 800 FT FROM THE APCH END OF RWYS 19; WE WERE ADVISED TO CONTACT TWR. WE ACKNOWLEDGED; AND CONTINUED TAXIING. I WAS GOING THROUGH AN EXPLANATION OF THE TKOF THAT MY INSTRUCTOR HAD GIVEN ME. WHEN I HAD FINISHED; WE WERE JUST PULLING INTO A HOLD SHORT POS. WE THEN SWITCHED TO TWR FREQ. I THEN HEARD THE CTLR SAY WHAT I PERCEIVED AS OUR ACFT NUMBER AND THE CLRNC 'CLRED FOR TKOF; RWY 19L; FLY RWY HDG; I'LL CALL YOUR R TURN.' I THEN REPEATED BACK OUR CALL SIGN AND 'CLRED FOR TKOF; ON THE L' AS WE ROLLED ONTO THE RWY AND ADDED PWR. WHEN WE WERE APPROX 500 FT AGL ON THE UPWIND; WE WERE ADVISED BY TWR THAT SHE DIDN'T RELEASE US FOR TKOF. SHE THEN INSTRUCTED US TO CONTACT RADAR ADVISORIES; WHICH WE DID. THE FLT CONTINUED UNEVENTFUL TILL TERMINATION. IN RETROSPECT; I THINK THE PROB COULD POSSIBLY HAVE BEEN AVOIDED BY TUNING IN TWR SOONER; OR BY NOT BEING HANDED OFF PREMATURELY. SECONDLY; I SHOULD HAVE INSISTED ON AN ANSWER TO MY QUERY 'CLRED FOR TKOF ON THE L.' IT IS UNCLR WHY THE CTLR USED OUR CALL SIGN ON CALL UP; WHICH I BELIEVE SHE DID. ATTN TO DETAIL AND MORE CARE IN ASCERTAINING CLRNCS COULD HAVE HELPED AS WELL.