AN ACR B737 FLC TURNED OFF THE RWY AT THE CORRECT TXWY THEN CUT IN FRONT OF ANOTHER ACFT THAT THE CAPT 'ASSUMED' WAS HOLDING FOR THEM.

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ON LNDG RWY 10; BWI; AT NIGHT; DAMP RWY; DECELERATING FOR TURNOFF AT TXWY E; WERE ISSUED INSTRUCTIONS TO TURN OFF ON TXWY E; TAXI ONTO TXWY P AND CONTACT GND. IN THE MIDST OF CHANGING CTL OF ACFT (FO MADE LNDG) WE RESPONDED 'ROGER' AND COMPLIED. EXITING; I SAW AN ACFT ON MY R; ON WHAT I ASSUMED WAS TXWY P. I ALSO ASSUMED THE ACFT WAS STOPPED FOR US; THE EXITING ACFT AS FO WAS CONTACTING GND. I ENTERED THE RAMP DIRECTLY AHEAD AND ADJACENT TO OUR INTENDED GATE. ON DOING SO I REALIZED THE ACFT I SAW WAS ON A CLOSE PARALLEL TXWY A. GND ASKED US TO CALL TWR ON THE PHONE. WE DISCUSSED THE SIT; I APOLOGIZED FOR THE CONFUSION; ASSURED THEM I SAW THE OTHER ACFT AND IN THE BRIEF MOMENT AT HIGH WORKLOAD PROCEEDED TO THE RAMP AREA. IN AN AREA ON THE ARPT WITH HIGH POTENTIAL FOR CONFLICT; AND AT A TIME OF VERY HIGH WORKLOAD FOR LNDG ACFT; AND NIGHT CONDITIONS; IT WOULD BE BETTER FOR THE LOW WORKLOAD ACFT (TAXIING) TO MAKE ADJUSTMENTS (IE; HOLD POS MOMENTARILY) THAN FOR THE RWY CLRING ACFT TO DO SO.