CONFLICT GND CRITICAL BETWEEN TWO TAXIING ACR LGTS.

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UPON LEAVING GATE; GND CTL INSTRUCTED FLT LGT TO TAXI TO RWY 27L VIA TXWY R; HOLD SHORT OF RWY 27R. TXWY R IS DIRECTLY AT THE END OF CONCOURSE D & C. AS WE PROCEEDED; ACR B APCHED FROM OUR LEFT AT AN EXCESSIVE TAXI SPEED. BELIEVING ACR B WAS NOT GOING TO STOP; I WAS FORCED TO APPLY MY BRAKES TO AVOID A COLLISION. I WAS ADVISED BY GND CTL AFTER MY ABRUPT STOP; THAT I WAS 'SUPPOSED TO BE AHEAD OF ACR B'. NOW I WAS TO FOLLOW A SECOND AIRPLANE; AN SMT TO RWY 27L. I ASKED THE CTLR WHAT INSTRUCTIONS HE HAD GIVEN ACR B? HE SAID HE WAS TOLD TO TAXI TO RWY 27L; HOLD SHORT OF 27R. NO INSTRUCTIONS WERE GIVEN TO EITHER LGT OR ACR B AS TO WHO WAS TO FOLLOW WHOM. AFTER FALLING IN BEHIND THE SMT I ASKED FOR A GND LINE NUMBER SO THAT I MIGHT FOLLOW THROUGH TO SEE IF A BETTER EXPLANATION MIGHT BE FORTHCOMING. AFTER GIVING ME A NUMBER; THE GND CTLR INSTRUCTED ME TO TAXI ACROSS RWY 27R. AFTER SPOOLING UP AND PARTIALLY XING THE HOLD LINE; HE TOLD ME TO CANCEL THE XING CLRNC AND TO HOLD SHORT FOR LNDG TFC. AGAIN I HAD TO SLAM ON MY BRAKES AND JEOPARDIZE THE SAFETY OF MY CREW AND AIRPLANE.