AN MD80 CREW; TAXIING FOR TKOF AT DFW; USED A TXWY NOT AUTH BY ATC.

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ON TAXI OUT AT DFW; GND CTL INITIALLY ADVISED US TO TAXI TO RWY 17R VIA STANDARD RTE (WHICH WOULD BE TO EXIT VIA TXWY JY; TURN R ON TXWY Y; THEN L ON TXWY L AND HOLD SHORT VIA TXWY EH AND MONITOR TWR ON 126.55 N OF TXWY Y). AS WE BEGAN TO TAXI UP TXWY JY; GND REVISED HIS TAXI INSTRUCTIONS FOR US TO NOW TAXI VIA TXWY Z; L STANDARD RTE. THE FO READ BACK THE NEW TAXI INSTRUCTIONS AND CONFIRMED WITH ME THAT WE WERE TO NOW TURN R ON TXWY Z; THEN A L ON TXWY L; THEN CONTINUE ON TXWY L TO TXWY EH FOR DEP. I CONCURRED AND EXITED TXWY JY BY TURNING R ONTO TXWY Z. AS WE TAXIED E ON TXWY Z; I BEGAN A L TURN ONTO TXWY K. THE FO BROUGHT IT TO MY ATTN THAT IT APPEARED THAT I WAS TURNING ONTO TXWY K AND NOT TXWY L AS PREVIOUSLY CLRED. THE ACFT HAD ALREADY BEEN TURNED MORE THAN 45 DEGS ONTO TXWY K FROM TXWY Z. I CONCURRED AND RECOGNIZED THE ERROR; BUT HAD TAXIED TOO FAR ONTO TXWY K TO BE ABLE TO CORRECT THE ERROR AND ELECTED TO CONTINUE THE SHORT DISTANCE ON TXWY K; THEN TRANSITIONED TO TXWY L AFTER MAKING THE QUICK R TURN ONTO TXWY Y. AS THIS EVENT OCCURRED; THERE WAS NO VISIBLE TFC ON EITHER SIDE OF OUR ACFT THAT WERE IN ANY POTENTIAL CONFLICT WITH THE INCORRECT TAXI RTE WHICH I FOLLOWED. SUPPLEMENTAL INFO FROM ACN 556047: AFTER TURNING R ONTO TXWY Z; I BEGAN TO RESUME ACCOMPLISHMENT OF THE REQUIRED BEFORE TKOF CHKLIST ITEMS. AS WE TAXIED E ON TXWY Z; THE CAPT BEGAN A L TURN ONTO TXWY K. AS HE INITIATED THIS TURN; MY EYES WERE INSIDE THE COCKPIT ACCOMPLISHING BEFORE TKOF ITEMS. AS WE HELD SHORT; THE CAPT ADVISED ME TO CONTINUE TO MONITOR TWR AS HE ATTEMPTED TO TALK WITH GND CTL ON THE SECONDARY FREQ. GND CTL WAS STILL BUSY AND DIDN'T APPEAR TO RECOGNIZE WHAT THE CAPT WAS TELLING HIM AND TOLD HIM TO MONITOR TWR.