A TAXIING LEAR 45 CROSSES THE HOLD SHORT LINE FOR RWY 6R IN VIOLATION OF THEIR TAXI CLRNC AT CLE; OH.

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CLE APCH CTL CLRED US FOR THE VISUAL TO RWY 6L AND TO CONTACT THE TWR. I (PIC/PNF) CONTACTED THE TWR AND WAS TOLD BY TWR; 'CLRED FOR TKOF.' I TOLD TWR WE WERE ON VISUAL FOR LNDG RWY 6L. TWR THEN TOLD US; 'CLRED TO LAND RWY 6L.' AFTER LNDG; WE TURNED OFF AT TXWY Z AND I ADVISED TWR WE WERE GOING TO THE S CARGO RAMP. TWR ADVISED US TO TURN OFF AT TXWY N AND HOLD SHORT OF RWY 6R. TXWY N IS AT THE OPPOSITE END OF THE RWY WE LANDED ON. AT THIS POINT; IT WAS CLR TO ME THAT THE TWR CTLR HAD US CONFUSED WITH ANOTHER ACFT OR WAS CONFUSED WITH HIS RWY DIRECTIONS. 'TURN OFF AT TXWY N AND HOLD SHORT OF RWY 6R' WOULD HAVE BEEN APPROPRIATE INSTRUCTION FOR A LNDG ON RWY 24R. TWR THEN CORRECTED HIMSELF AND TOLD US TO TAXI ON TXWY Z AND HOLD SHORT OF RWY 24L. AT THIS TIME; I WAS HEADS DOWN REVIEWING THE TAXI CHART TO VERIFY OUR POS ON TXWY Z AND RWY 24L. AS I THEN LOOKED UP; I SAW THE HOLD LINE FOR RWY 24L COMING UP AND IMMEDIATELY TOLD THE FO; WHO WAS TAXIING THE ACFT; TO 'STOP.' AT THE SAME TIME; THE TWR CTLR ALSO TOLD US TO 'STOP.' WE DID STOP; BUT THE ACFT'S NOSE; AND POSSIBLY THE NOSEWHEEL; HAD CROSSED THE HOLD SHORT LINE. NO ACFT HAD TO ABORT OR GO AROUND DUE TO THIS INCIDENT. TWR TOLD US THEN TO CROSS RWY 24L AND CONTACT GND ON THE OTHER SIDE. WE DID AND TAXIED TO OUR DEST. APPARENTLY; THE TWR CTLR WAS VERY BUSY WITH DEPARTING TFC ON RWY 6R -- SINCE I SAW QUITE A LINE OF ACFT FOR DEP AS WE WERE MAKING OUR APCH TO RWY 6L. WE MAY HAVE BEEN THE ONLY ARRIVING ACFT AT THIS TIME. THE TWR CTLR'S ATTN MAY HAVE BEEN MORE ON HIS NUMEROUS DEPS THAN ON US. THE COMS ERRORS AND CONFUSING INSTRUCTIONS FROM HIM CAUSED CONFUSION FOR US; ESPECIALLY IN ME BEING HEADS DOWN WITH THE TAXI CHART TO SORT OUT WHAT THE CTLR WANTED US TO DO. ADDITIONALLY; THE FO; WHO WAS TAXIING THE ACFT; MAY HAVE BEEN DISTR FROM PAYING CLOSE ATTN TO TAXIING BY THE CONFUSING TWR INSTRUCTIONS.