FLC OF AN ACR LTT ACFT INADVERTENTLY TRANSGRESSED A PARALLEL RWY DURING ROLLOUT AFTER LNDG ON THE OTHER PARALLEL RWY CAUSING ANOTHER ACFT TO BE ABORTED BY ATC FOR SAFETY PRECAUTIONS.

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ON MAY/XX/93 WE WERE ON OUR WAY TO BULLHEAD CITY; AZ (P06) FROM FARMINGTON; NM; ON A MAINT FLT. ABOUT 1/2 WAY TO BULLHEAD CITY OUR COMPANY REACHED US AND TOLD US TO CONTINUE ON TO LAX. UPON REACHING LAX AND LNDG ON RWY 25L I STATED TO THE TWR CTLR THAT WE WERE UNFAMILIAR AND NEEDED TO KNOW WHICH WAY TO TURN OFF THE RWY FOR THE TERMINAL. THE CTLR TOLD US TO TAKE THE NEXT R HIGH SPD EXIT. AS WE STARTED TO TURN; HE CAME BACK AND TOLD US TO EXPEDITE TO THE NEXT L REVERSE HIGH SPD BECAUSE OF TFC SHORT FINAL BEHIND US. UP UNTIL THIS POINT MY FO HAD CTL OF THE AIRPLANE. I TOOK THE AIRPLANE FROM HIM AND STARTED TO PWR UP A BIT TO EXPEDITE TO THE NEXT L REVERSE HIGH SPD; WHICH APPEARED TO BE 1000-2000 FT DOWN THE RWY. AS WE WERE EXPEDITING THE CTLR TOLD US INSTEAD TO TAKE THE NEXT R HIGH SPD AND HOLD SHORT OF RWY 25R DUE TO THE FACT THAT THE TFC BEHIND US WAS NOW ON VERY SHORT FINAL. I ACKNOWLEDGED AND STARTED TO TURN R ON THE HIGH SPD EXIT WHICH WE WERE ALMOST ADJACENT TO. I PUT THE AIRPLANE IN FULL BETA; GOT ON THE BRAKES AND DID STOP WELL SHORT OF THE RWY. I BELIEVE WE STOPPED PRIOR TO THE HOLD BARS; HOWEVER; THE CTLR HAD THE ACFT DEPARTING RWY 25R ABORT ITS TKOF AND THEN TOLD US TO CONTINUE ACROSS RWY 25R AND INTO PARKING. WE HAD INFORMED THE CTLR THAT WE WERE UNFAMILIAR AND IN RETURN WERE TOLD 3 DIFFERENT EXIT INSTRUCTIONS 3 DIFFERENT TIMES. THIS; COUPLED WITH FINALLY HAVING TO EXPEDITE ONTO A HIGH SPD EXIT THAT ENDED ABRUPTLY AT THE PARALLEL RWY; CONTRIBUTED TO THE PROB. IN TRYING TO ACCOMMODATE US; THE CTLR ONLY ADDED TO THE CONFUSION. WE DID OUR BEST TO ACCOMMODATE HIM AND TO CLR THE RWY ASAP; AWARE THAT WE HAD TFC LNDG SOMEWHERE BEHIND US. PERHAPS WE BOTH SHOULD HAVE PAID MORE ATTN TO THE FACT THAT WE WERE AT AN UNFAMILIAR; BUSY ARPT; AND REQUIRED EXTRA TIME AND HANDLING.