FLC OF AN LGT ACR ACFT STARTED TKOF ROLL UPON CLRNC TO ANOTHER ACFT ON A CROSS RWY RESULTING IN THE TWR INTERVENING AND THE RPTRS ABORTING THE TKOF.

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TAXIING OUT AT BOS WE WERE CLRED TO RWY 22R. AN ACR Y FLT REFUSED RWY 22R; WAS OFFERED 22L AND REFUSED -- TOO HVY. ACR Y WAS CLRED TO 15R WITH 'AT LEAST 30 MIN DELAY FOR TKOF.' AFTER ABOUT 7 DEPS BEFORE US ON 22R AND 22L WE WERE CLRED INTO POS ON 22R. AFTER A FEW SECONDS IN POS WE WERE CLRED FOR TKOF (WE THOUGHT). I LISTENED CAREFULLY TO THE FO READBACK OF THE TKOF CLRNC; AND FO STARTED TKOF ROLL. PROMPTLY (WE WERE BELOW 70 KT). THE TWR SAID SOMETHING LIKE 'ACR X THAT TKOF CLRNC WAS NOT FOR YOU; STOP YOUR TKOF.' FO CLOSED THE THROTTLES. I TOOK CTL AND SLOWED ACFT. I WAS AN ACR Y ROLLING ON RWY 15R. TWR CLRED US TO MAKE A 180 ON THE RWY AND TAXI BACK FOR TKOF. WE WERE CLRED FOR TKOF AND MADE AN UNEVENTFUL DEP. WE TALKED ON THE PHONE TO THE SUPVR OF BOS TRACON WHEN WE ARRIVED IN LAX. IT APPEARS TWR CLRED ACR Y FOR TKOF AND THE FO AND I PERCEIVED IT AS CLRNC FOR US; ACR X; TO TKOF. ACR Y AND WE MUST HAVE READ BACK THE CLRNC AT THE SAME TIME. AN EXCELLENT CATCH BY AN ALERT CTLR! WE HAD FORGOTTEN ABOUT THE ACR Y ON 15R AND THERE WAS NO ACFT WAITING FOR 22L. WE APPARENTLY 'HEARD' WHAT WE EXPECTED.