CAPT OF ACR WDB ACFT LOST CTL OF THE ACFT DURING LNDG ROLL HIGH-SPD TURNOFF.

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FO'S APCH AND LNDG ON 25L AT LAX INTL. WDB TKOF ON 25R 1 MIN PRIOR TO OUR TOUCHDOWN; SO FO CARRIED REF SPD PLUS 10 KTS (VORTICES ANTICIPATION). TOUCHDOWN APPROX 2000 FT DOWN RWY AT ABOUT 130 KTS. USED PARTIAL REVERSE (CLAIMED #2 ENG CAME IN FASTER THAN #1 AND #3 ENGS). STARTED FOR SECOND HIGH-SPD TURNOFF TO TAXIWAY 45. AFTER 100 KTS CALL BY ME; I NOTICED BRAKING AT 90-95 KTS AND ACFT SEEMED TO BE DECELERATING AT A NORMAL RATE. CALLED 'I'VE GOT IT' AT 80 KTS WITH PLAN TO STOP BY 25R PER TWR INSTRUCTIONS. AS WE ENTERED HIGH-SPD TAXIWAY; ACFT SEEMED TO LOCK BRAKES AND SHUDDERED VIOLENTLY WITH LOSS OF DIRECTIONAL CTL; SLIDING TOWARDS EDGE OF TAXIWAY. APPLIED MORE R RUDDER AND NOSEGEAR STEERING WITH DIRECTION REGAINED AT ABOUT 15 KTS AND ACFT NEARLY BROUGHT TO A STOP -- HOWEVER; INCURSION INTO 25R COULD NOT BE AVOIDED (10-15 FT) -- TWR SAW THIS; AND CLRED US TO CROSS 25R; HOLDING ACFT IN TKOF POS. THE TWR ALSO CALLED FIRE DEPT; CLAIMING TO HAVE SEEN SMOKE AND POSSIBLY FLAMES FROM NOSE GEAR AREA. TAXIED ACROSS 25R ONTO OUTER FACING W TO AWAIT FIRE TRUCKS AS PER TWR'S INSTRUCTION. FIRE DEPT INSPECTED NOSE GEAR; ADVISED ONLY BALD TIRE R NOSEWHEEL AND OK TO TAXI -- TAXIED TO GATE. NO INJURIES; NO ACFT DAMAGE. MAINT INSPECTED BRAKES AND ANTI-SKID; REPLACING ONLY R NOSE GEAR TIRE. WITH 14 YRS ON THIS ACFT; HAVE NEVER SEEN ANY INCIDENT OF THIS SORT! DID NOT FEEL TURNOFF SPD WAS HIGH AND NEVER DOUBTED ABILITY TO STOP SHORT OF 25R UNTIL SHUDDERING AND LOSS OF STEERING CTL. IN HINDSIGHT; WILL BRIEF 'NO COMMITMENT TO TURNOFF TAXIWAY UNTIL 60 KTS' AND THEN WILL TAKE CTL. ALSO BRIEF MORE USE OF REVERSERS (90% TARGET).