TXWY UNAUTH TKOF BY STUDENT PLT.

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I DEPARTED SAN PATRICIO COUNTY ARPT (T69); SINTON; TX; IN A CESSNA 150 ON THE 1ST LEG OF A SOLO XCOUNTRY BOUND FOR MCALLEN MILLER INTL (MFE); MCALLEN TX. THE ENRTE FLT FROM SINTON TO MCALLEN WAS ROUTINE AND WITHOUT INCIDENT. THE WX WAS GENERALLY GOOD VFR BUT BECAME A LITTLE HAZIER AS I APCHED MCALLEN. I WAS GIVEN RADAR VECTOR ASSISTANCE AND LOCATED THE ARPT ABOUT 4 MI AWAY AT MY 11 O'CLOCK POS. I WAS INSTRUCTED TO CONTACT THE TWR AND I DID. I WAS CLRED TO LAND ON RWY 13 AND I COMPLIED. FOLLOWING THE LNDG; I WAS INSTRUCTED TO DEPART THE RWY ON TXWY BRAVO. I REQUESTED THAT GND CTL PROVIDE ME WITH PROGRESSIVE TAXI INSTRUCTIONS TO FBO. I TAXIED TO FBO AND REFUELED. AT THE TIME OF MY DEP THE TWR HAD CHANGED THE RWY FROM RWY 13 TO RWY 31. I ONCE AGAIN ASKED FOR PROGRESSIVE TAXI INSTRUCTIONS FROM MCALLEN GND CTL. AS I WAS TAXIING OUT ON TXWY CHARLIE THE VOICE OF GND CTLR WAS THAT OF A WOMAN. I TAXIED OUT TO THE INTXN OF TXWY CHARLIE AND TXWY ALPHA WHICH RUNS PARALLEL TO THE ACTIVE RWY 31. AS I WAS APCHING THE INTXN; THE VOICE ON THE RADIO CHANGED FROM THAT OF A WOMAN TO THAT OF A MAN. IN THINKING BACK UPON WHAT HAPPENED NEXT; I MUST HAVE MENTALLY MADE AN ASSUMPTION THAT I WAS NOW TALKING TO THE CTL TWR RATHER THAN GND CTL. I CANNOT RECALL IF I CHANGED FREQ ON THE RADIO. HAVING THE BENEFIT OF SUBSEQUENTLY REVIEWING WHAT HAPPENED AT MCALLEN IN A TELEPHONE CONVERSATION WITH MCALLEN TWR; I NOW KNOW THAT I WAS ASKED IF I WANTED TO USE THE ENTIRE RWY OR IF I WOULD ACCEPT AN INTXN TKOF. (IN WHICH I WOULD HAVE BEEN REQUIRED TO TAXI STRAIGHT AHEAD ACROSS TXWY ALPHA; THEN TURN R DOWN RWY 31 AND TKOF.) THE MCALLEN TWR TOLD ME ON THE TELEPHONE THAT I DIDN'T REPLY WHEN I WAS ASKED IF I WANTED AN INTXN TKOF; AND I PROBABLY DID NOT SINCE I HAD NEVER MADE AN INTXN TKOF AND WAS CONFUSED AT THIS TIME. WHAT I DON'T UNDERSTAND IS HOW THE TWR OR GND CTL COULD ASSUME I UNDERSTOOD WHAT WAS XMITTED IF I DIDN'T REPLY. I WAS ASKED IF I WAS READY FOR TKOF AND REPLIED THAT I WAS. I WAS ASKED THIS SAME QUESTION A SECOND TIME AND AGAIN A THIRD TIME; AND BOTH TIMES I REPLIED IN THE AFFIRMATIVE. WHEN THE TWR OPERATOR ASKED ME THE THIRD TIME; BEING CONFUSED; I MUST HAVE ASSUMED THIS WAS HIS WAY OF TELLING ME I WAS CLRED FOR TKOF. I WAS REALLY CONFUSED AND INTIMIDATED. WHEN HE ASKED ME THE THIRD TIME IF I WAS READY FOR TKOF; I REPLIED YES AND RELEASED THE BRAKES; TURNED TO THE R TO A HDG OF 310 DEGS. TXWY ALPHA IS A WIDE AND LONG TXWY AND COMPARES TO THE RWY I USED FOR THE SIGNIFICANT PART OF MY TRAINING. AS SOON AS I ROTATED AND WAS LIFTING OFF I REALIZED I HAD MADE A MISTAKE AND TAKEN OFF FROM A TXWY BECAUSE OF THE CONTINUOUS YELLOW LINE DOWN THE TXWY. THERE WAS NO TFC ON RWY 31 OR ON TXWY ALPHA IN FRONT OF ME. BECAUSE THE OF FACT THAT I WAS ALREADY AIRBORNE; I DECIDED TO CONTINUE AND TO LINE UP WITH RWY 31. I LOOKED BACK BEHIND ME AND IN FRONT AND SAW NO ACFT DEPARTING FROM RWY 31. I BANKED THE ACFT L; FLEW OVER TO RWY; AND THEN TURNED TO THE R TO ALINE THE ACFT WITH RWY 31. I CONTINUED TO CLB STRAIGHT OUT ON A HDG O 310 DEGS WHICH IS THE HDG TO LAREDO INTL ARPT. AS I WAS CLBING OUT; I WAS CONTACTED BY RADIO ON THE SAME FREQ I USED PRIOR TO TKOF (I NOW REALIZE IT; I STILL DON'T KNOW IF IT WAS GND CTL OR TWR) AND NOTIFIED THAT I HAD MADE AN UNCLRED TKOF AND THAT I HAD TAKEN OFF FROM A TXWY (THIS I ALREADY KNEW). I WAS GIVEN A TELEPHONE NUMBER AND ASKED TO CALL MCALLEN TWR WHEN I REACHED MY NEXT DEST AT LAREDO INTL. MY FLT INSTRUCTOR CONTACTED MR. X OF THE SAN ANTONIO FSDO AND REVIEWED THIS MATTER WITH HIM. MY FLT INSTRUCTOR AND I HAVE MADE PLANS TO FLY ADDITIONAL DUAL AT AN ARPT WITH A CTL TWR AND WILL PROBABLY DO SO WITHIN 10 DAYS IF THE WX ALLOWS.