FK10 CREW WAS SLOW IN ESTABLISHING COM WITH GND CTLR.

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TAXI INCIDENT IN WHICH MY ACFT WAS EXITING RWY 28L TO THE N VIA HIGHSPD TXWY. NORMALLY; TWR DIRECTS AN INITIAL TAXI RTE. I AWAITED THIS AND HEARING NONE; LOOKED DOWN TO MY L AT ACARS TO REFRESH MEMORY AS TO GATE; THEN CALLING TO 'JOG' TWR AS TO DIRECTING EITHER TO GND FREQ OR ASSIGNING TAXI INSTRUCTIONS. AS I LOOKED UP AND BEGAN XMITTING; THE CAPT; ALTHOUGH SLOWED; HAD CONTINUED TO TAXI TOWARD THE JUNCTURE OF THE HIGH SPD/PARALLEL TXWY. I NOTICED THAT A COMMUTER ACFT HAD APPARENTLY OVERTAKEN US ON THE PARALLEL. WE HAD NOT NOTICED THIS ACFT BEING POSITIONED WITHIN NORMAL SPD TAXI DISTANCE OF THE TXWY INTXN WITH THE HIGH SPD. THE TWR; AFTER A MOMENT'S DELAY FROM HEARING MY XMISSION OF 'XXXX HAS GATE XX;' RESPONDED WITH A DIRECTION OF 'TURN R ON TXWY T; CROSS RWY 28C; VICTOR XX; TO THE RAMP.' AS I WAS READING BACK WE WERE NEARLY TO THE INTXN OF THE PARALLEL AND I NOTICED THE DH8 OR DORNIER COMMUTER ACFT TAXIING TOWARD MY ACFT ON THE PARALLEL AND IT APPEARED TO BE STOPPING SOMEWHAT ABRUPTLY TO AVOID CONFLICT. THE CAPT OF MY ACFT (WHO ACCOMPLISHED BOTH THE LNDG AND TAXIING TASKS) AND I BOTH NOTICED THE OTHER ACFT AT THE SAME TIME AND BEGAN BRAKING AND WITH SEEING IT STOPPING AND RECEIVING THE CLRNC; CONTINUED. I SHOULD MAKE BETTER EFFORT TO CLR ALL POSSIBLE TFC TO THE SIDE AND AFT OF A TURN IN MY DIRECTION BEFORE LOOKING DOWN. PERSON TAXIING SHOULD STOP EXITING RWY UNTIL CLRNC IS RECEIVED.