AN ACR B737 FLC STAYED ON RWY 28 DURING THEIR TAXI ACROSS RWY 23L AND INTO POS ON RWY 23R INSTEAD OF USING TXWY Z. THE ATCT LCL CTLR WAS CONCERNED THAT THE FLC KNEW THAT THEY WERE ON RWY 28 INITIALLY AND LATER THAT THEY WERE NOT AT THE VERY END OF RWY 23R.

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CLEVELAND HAS A VERY CONFUSING AREA NEAR RWYS 28/23L/R FOR TAXI OPS. WE WERE CLRED TO TAXI VIA THE RWY 28 HOLD SHORT OF RWY 23L CALL TWR. AS WE HELD SHORT GND SWITCHED US TO THE TWR. THEN TWR GAVE US CLRNC TO RWY 23R POS AND HOLD. WE DID JUST THAT VIA RWY 28 TO CROSS RWY 23L AND POS AND HOLD RWY 23R AT RWY 28. TWR TOLD US THAT WE WERE ON RWY 28 WHICH WE ROGERED AND ASKED IF WE COULD DEPART FROM RWY 28 ON RWY 23R. TWR THOUGHT WE WOULD TAXI VIA TXWY Z TO RWY 23R; BUT DID NOT SPECIFY WHICH RTE TO TAKE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT HE AND HIS CAPT DO NOT OFTEN OPERATE THROUGH CLE AND THE LIGHTING SYS AND TXWYS WERE NEW TO THEM. THE FO SAID THAT THE NEW FLASHING HOLD LINE AT RWY 23L ON RWY 28 AND THE NEW CTRLINE TAXI LIGHTS ON RWY 28 ARE A GREAT AID; PARTICULARLY AT NIGHT. ALTHOUGH THE FLC DISCUSSED THE VARIOUS POTENTIAL TAXI ROUTES TO RWY 23R THEY DID NOT KNOW THAT THE CTLR INTENDED THEM TO TURN TO THE R AND USE TXWY Z TO GET TO RWY 23R AND HE DOES NOT RECALL THE CTLRS MENTIONING TXWY Z. AFTER TKOF THEY DID DISCOVER THAT THEIR DATA WAS BASED ON USING ALL OF THE RWY ALTHOUGH THE INTXN WAS MORE THAN ADEQUATE. AFTER ARR AT THEIR DEST THE CAPT CALLED THE CLE TWR AND SPOKE TO A SUPVR. ALLEGEDLY; THE SUPVR TOLD THE CAPT THAT THE CTLR'S ONLY CONCERN WAS THAT THEY NOT ATTEMPT A TKOF ON RWY 28. OTHERWISE THE SUPVR WAS NOT CONCERNED ABOUT THE INTXN TKOF.