BAE3201 CREW EXPERIENCED THE ACFT DEPART THE RWY WHEN THEY ATTEMPTED TO MAKE A RWY TURNOFF REQUESTED BY THE TWR.

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I WAS THE CAPT AND PF ON ACR FLT XXX FROM IAD TO LYH ON JUN/FRI/98. I WAS ASSISTED BY FO YYY; THE PNF. THE ACFT WAS J32; #ZZZ. THE FLT DEPARTED IAD ON AN IFR FLT PLAN. ON DSCNT INTO LYH; CTR CLRED US FOR THE VISUAL TO RWY 21 AFTER WE CALL THE FIELD IN SIGHT. WE WERE HANDED OFF TO LYH TWR. LNDG CHKS WERE COMPLETED AND TWR CLRED US TO LAND. WHEN WE WERE BTWN 500-800 FT AGL; TWR ASKED IF WE COULD MAKE TXWY D FOR TFC; BUT STATED IT WAS NOT REQUIRED. THE FO ACKNOWLEDGED THE CALL. LNDG WAS NORMAL AND IN THE TOUCHDOWN ZONE. AFTER THE FO CALLED 2 BETAS LIGHTS; I WENT INTO REVERSE. THEREAFTER; I MADE AN INITIAL BRAKE APPLICATION AND THE ACFT PULLED SLIGHTLY TO THE R. I RELEASED THE BRAKES AND DETERMINED WE WOULD NOT BE ABLE TO MAKE THE TXWY D TURNOFF. UPON FURTHER APPLICATION OF THE BRAKES; THE R BRAKE APPEARED TO LOCK AND WE VEERED MORE SEVERELY TO THE R. I WAS ALSO APPLYING L BRAKE AND L STEER WITH THE TILLER IN AN ATTEMPT TO COUNTERACT THE VEER TO THE R. HOWEVER; THERE WAS NO CHANGE IN DIRECTION. I GOT ON THE BRAKES HARDER BUT COULD NOT STOP BEFORE WE LEFT THE RWY SURFACE. AT THIS POINT I HAD TO TURN TO THE R TO AVOID HITTING THE TXWY SIGN. THE ACFT CAME TO A STOP. I CALLED FOR THE EMER EVAC MEMORY ITEMS AND SET THE PARKING BRAKE. WE CALLED FOR THE CRASH EQUIP. A JUMP-SEATING J32 CAPT CAME FORWARD AND SAID THE BACK WAS SECURE AND THAT HE HAD THE PAX UNDER CTL. THE FO AND I FINISHED SHUTDOWN IN THE COCKPIT; AND THEN HE BEGAN TO DEPLANE THE PAX. WE DEPLANED THE PAX AND THE FO KEPT THEM TOGETHER AND OFF THE RWY. I RETURNED TO THE COCKPIT AND REVIEWED THE QRH TO MAKE SURE THE NECESSARY STEPS WERE COMPLETE. THIS ALSO OCCURRED AFTER A 'REDUCED REST OVERNIGHT.' CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT SUSTAINED NO DAMAGE OF ANY KIND. THE R TIRES WERE NOT BLOWN NOR WERE THERE ANY FLAT SPOTS ON THEM. THE RWY WAS DRY. THE CAPT RPTS; IT IS COMMON KNOWLEDGE ON HIS AIRLINE THAT THE BAE3201 ACFT HAS MARGINAL TO POOR BRAKES. THE MOST COMMON PROB IS GRABBING BRAKES. THE CAPT ATTRIBUTES THIS TO MAINT NOT PROVIDING ANY MEANINGFUL CORRECTIVE ACTION WHEN BRAKES ARE WRITTEN UP FOR 'GRABBING.' IN FACT; IN THIS INCIDENT; EVEN THOUGH THE ACFT LEFT THE RWY; MAINT ONLY FOUND THE BRAKE SYS 'OK FOR SVC.' THE CAPT RPTED HE COMPLETELY RELEASED THE R BRAKE. MAX BRAKING ON THE L BRAKE AND APPROPRIATE NOSEWHEEL STEERING WERE UNABLE TO OVERCOME THE DRAGGING R BRAKE; WHICH CAUSED THEM TO LEAVE THE RWY.