CONFLICT BETWEEN 2 MLG'S WHEN THE PRECEDING ACFT TURNED IN FRONT OF THE SECOND MLG ON GO AROUND OVER RWY 8R.

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PHX TWR INSTRUCTED US TO TAXI INTO POS AND HOLD AND TO MAINTAIN VISUAL ON THE DEPARTING LGT. THE LGT WAS JUST BEGINNING ITS TKOF ROLL ON RWY 8R. TWR THEN INSTRUCTED US TO BE READY FOR AN IMMEDIATE DEP. AS THE LGT ROTATED WE WERE CLRED FOR TKOF. WHILE ACCELERATING THROUGH ABOUT 80-90 KTS; I HEARD PHX TWR INSTRUCT MLG Y ON FINAL TO GO AROUND AND TO DISPLACE TO THE RIGHT (S) SIDE OF THE RWY. AFTER WE ROTATED PHX TWR INSTRUCTED US TO PROCEED DIRECT TO RIO SALADO BEACON (OUR NORMAL PROC). TWR THEN INSTRUCTED THE GO AROUND ACFT TO MAINTAIN RWY HDG AND TO MAINTAIN VISUAL SEP ON US. AS WE APCHED THE RIO SALADO BEACON WE HAD NOT BEEN HANDED OFF TO DEP CTL. I THEN ASKED TWR IF HE WANTED US TO SWITCH TO DEP CTL. TWR THEN SENT US TO DEP ON 124.1. DURING THE SWITCH WE HAD PASSED THE RIO SALADO BEACON AND HAD STARTED OUR TURN TO INTERCEPT THE SRP 168 DEG R AS FILED ON THE STANFIELD 1 DEP. UPON CHKING IN ON DEP FREQ; WE WERE INSTRUCTED TO TURN LEFT 090 DEGS IMMEDIATELY. WE NEVER SAW THE CONFLICTING ACFT AND I DON'T KNOW HOW CLOSE WE CAME TO HIM; BUT JUDGING FROM THE SOUND OF HIS VOICE WHEN HE REQUESTED OUR CALL SIGN FROM DEP CTL; IT WAS EVIDENT THAT HE WAS NOT HAPPY WITH US OR THE HANDLING HE RECEIVED. I CAN APPRECIATE PHX TWR'S EAGERNESS TO EXPEDITE TFC; BUT WHEN THE TEMP IS HIGH AND ACFT ARE HVY IT TAKES A LITTLE MORE TIME TO GET INTO THE AIR. THIS SOMETIMES RESULTS IN AN UNTIMELY GO AROUND. WHEN THIS HAPPENS; HOWEVER; TWR SHOULD HAVE A BETTER PLAN TO PREVENT THIS TYPE OF CONFLICT.