A C208 SINGLE PLT DEPARTED CAE WITHOUT PERMISSION.

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AT COLUMBIA METRO ARPT LOCATED IN COLUMBIA; SC; I WAS GIVEN PERMISSION TO TAXI TO RWY 5 AT THE INTXN OF TXWY F. RWY 11 WAS BEING USED FOR DEPS BY PAX CARRYING JETS. I REQUESTED RWY 29 BUT IT WOULD CAUSE A DELAY FOR ME; SO THE CTLR SUGGESTED RWY 5 AT TXWY F. WHEN I APCHED THIS LOCATION I CALLED UP TWR AND ADVISED HIM THAT I WAS READY TO TAKE OFF. HE GAVE ME THE INSTRUCTION TO TAXI INTO POS AND HOLD. I REPEATED TAXI AND HOLD AND; AS I TURNED ONTO THE RWY; IT LOOKED SHORTER THAN IT ACTUALLY IS BECAUSE THE LAST PART OF THE RWY SLOPES DOWN. JUST AS I WAS GETTING INTO POS ON THE RWY I MADE SURE THAT THE FREQ WAS CLR AND QUICKLY ASKED HOW MUCH RWY WAS REMAINING FROM THAT INTXN. A FEW SECONDS WENT BY AND I HEARD A LITTLE DISTORTION ON THE FREQ BUT IT WAS NOT RECOGNIZABLE AS A XMISSION FROM THE TWR TO ANYONE ELSE OR ANYONE ELSE TO THE TWR; I DID NOT HEAR ANY WORDS AT ALL. AT THIS POINT I WAS HOLDING ON THE RWY WAITING TO TAKE OFF. A SECOND LATER I HEARD THE TWR SAY '4000 FT' AND IMMEDIATELY AFTER THAT; 'CLRED FOR TKOF.' HE DID NOT SAY MY CALL SIGN; CLRED FOR TKOF; BUT I ASSUMED IT WAS FOR ME SINCE HE WAS JUST TALKING TO ME BY ANSWERING MY QUESTION AND IMMEDIATELY SAYING CLRED FOR TKOF. I TOOK THIS AS HIM REASSURING ME THAT I HAD ADEQUATE RWY AND TELLING ME I WAS ABLE TO TAKE OFF. I REALIZED THAT THERE WERE DEPS ON RWY 29; BUT ASSUMED THAT THEY WERE NOT READY FOR TKOF OR HOLDING IN POS AS WELL. IMMEDIATELY AFTER I THOUGHT I WAS GIVEN THE CLRNC TO TAKE OFF; I RESPONDED BY SAYING EITHER; CLRED FOR TKOF AND MY CALL SIGN; OR SIMPLY; CLRED FOR TKOF AND SHORTENED THE CALL SIGN. AS SOON AS I MADE THAT XMISSION I BEGAN TO ACCELERATE AND TOOK OFF RWY 5. THE TWR; AT NO POINT; CAME BACK AND TOLD ME TO ABORT TKOF OR CORRECTED ME THAT I WAS NOT CLRED TO TAKE OFF AND THAT THE CLRNC WAS FOR AN AIRPLANE ON RWY 29. AFTER REACHING ABOUT 300-400 FT; I WAS MORE THAN SURPRISED TO FIND OUT THAT I WAS NOT SUPPOSED TO TAKE OFF AND THAT THE CLRNC WAS; IN FACT; FOR A DIFFERENT PLANE. I DID NOT SPECIFICALLY QUESTION THE CTLR IF; IN FACT; I WAS THE ONE WHO WAS RECEIVING THE TKOF CLRNC FOR 2 REASONS: FIRST; I WAS CERTAIN THAT IT WAS FOR ME SINCE HE DID NOT USE THE CALL SIGN OF A DIFFERENT PLANE AFTER TELLING ME THE RWY LENGTH. SECONDLY; I CLRLY RESPONDED THAT I WAS TAKING OFF AND USED MY FLT NUMBER. I; HOWEVER; DID NOT SAY THE RWY NUMBER AS PART OF MY RESPONSE AS I NORMALLY DO. THE TWR EXPLAINED TO ME THAT THIS MIX-UP MIGHT HAVE BEEN CAUSED ONE OF US STEPPING ON A FREQ WHICH SOUNDS PLAUSIBLE TO ME SINCE I DID NOT HEAR THE AIRPLANE CALL SIGN BEFORE THE PHRASE '4000 FT; CLRED FOR TKOF.' HOWEVER; THERE WAS NO INTERRUPTION BTWN 4000 FT AND CLRED FOR TKOF AND IT SEEMED UNLIKELY TO ME THAT HE WOULD SAY THE CALL SIGN OF A JET; ANSWER MY QUESTION; AND GO BACK AND TELL THE JET TO TAKE OFF WITHOUT SPECIFICALLY SAYING WHO HE WAS TALKING TO. I BELIEVE THE PROB WAS BOTH ON MY SIDE AND THE CTLR'S. I SHOULD HAVE SPECIFICALLY VERIFIED THAT IT WAS I WHO WAS GIVEN THE CLRNC FOR TKOF AND THE CTLR SHOULD HAVE STOPPED ME WHEN I RESPONDED THAT I WAS TAKING OFF.