TXWY EXCURSION AFTER LOSS OF ACFT CTL.

Narrative

THE FO WAS FLYING AND MADE A NORMAL LNDG ON RWY 22L AT EWR. HE SLOWED THE ACFT USING NORMAL BRAKING. THE FO TRANSFERRED CTL OF THE ACFT AND I ACCEPTED AT THE USUAL POINT FOR USE OF THE STEERING TILLER FOR CLRING THE RWY AND TAXI TO THE RAMP. THIS EVENT OCCURRED DURING ONE OF THE MANY 'RUSH HRS' AT THE EWR AND THE TWR CTLR ASKED US TO EXPEDITE CLRING OF THE RWY FOR TFC ON SHORT FINAL BEHIND US. I ANGLED THE ACFT TOWARD TXWY G; A 90 DEG INTXN; OUR FIRST AVAILABLE EXIT FROM THE RWY AND A USUAL EXIT POINT FOR THIS ACFT; ESPECIALLY CONSIDERING WE WERE AT LEAST 8000 LBS UNDER MAXIMUM GROSS LNDG WT. TO EXPEDITE CLRING; I ENTERED THE TURN AT A MAXIMUM ACCEPTABLE SPD. AS I PUSHED THE BRAKE PEDALS; THEY BOTTOMED OUT WITH NO BRAKE APPLICATION. MY IMMEDIATE REACTION WAS TO OBSERVE THAT ALL 3 HYD PRESSURE GAUGES SHOWED NORMAL SYS PRESSURES. THE FO REALIZED I HAVE NO BRAKES AND TRIED HIS BRAKE PEDALS WITH THE SAME CONSEQUENCE. I CONSIDERED OUR SPD TOO HIGH TO SAFELY EXECUTE A TIGHTER TURN AND THEREFORE WE WERE UNABLE TO COMPLETE THE TURN ONTO THE TXWY. THE NOSEWHEEL LEFT THE PAVEMENT AND SHORTLY BROUGHT US TO A COMPLETE STOP. WE HAD TO BE TOWED BACK ONTO THE PAVEMENT. WITHIN SEVERAL HRS OUR MAINT DEPT HAD DETERMINED THAT THERE WAS NO HYD PRESSURE TO THE BRAKES BUT HAD BEEN UNABLE TO DETERMINE THE CAUSE. A POSSIBLE WAY TO HAVE AVOIDED THE INCIDENT WOULD HAVE BEEN TO BY-PASS THE FIRST AVAILABLE EXIT FROM THE RWY; 90 DEG 'G' AND TURNED AT THE NEXT TXWY; A 'HIGH- SPD' EXIT. USE OF TXWY 'G' IS NOT A UNREASONABLE EXPECTATION; EVEN AT MAXIMUM GROSS LNDG WT; AND WOULD HAVE BEEN UNEVENTFUL IN THIS SIT WITHOUT THE INTERRUPTION OF THE YET TO BE DETERMINED MALFUNCTION.