MD-80 CREW WAS GIVEN TKOF CLRNC ON RWY 32R AT THE SAME TIME AN RJ HAD LNDG CLRNC ON RWY 22R AT ORD. THE RJ WAS GIVEN A TWR DIRECTED GAR. THE RPTR ESTIMATED THE MISS DISTANCE AS 500 FT HORIZONTAL AND ZERO FEET VERTICAL.

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INTERSECTING RWY OPS ORD. WHILE TAXIING INTO POS TO HOLD ON RWY 32R AT ORD; WE WERE ASKED IF WE COULD ACCEPT AN IMMEDIATE TKOF AND WE ACCEPTED. STARTED OUR TKOF ROLL IMMEDIATELY. WE HEARD TWR INSTRUCT A ACFT CALL SIGN TO GAR AND MY FO LOOKED TO HIS RIGHT AND SAW AN RJ GOING AROUND FROM A LOW ALTITUDE. IT APPEARED THAT IF HE HAD NOT GONE AROUND WE MIGHT HAVE MET AT THE INTXN OF THE 2 RWYS; HE WAS LNDG RWY 22R. EVERYTHING WORKED OUT FINE BUT I AM NOT SURE WHY WE WERE BOTH GIVEN CLEARANCES. WE WERE NEVER MADE AWARE OF THE APCHING ACFT TO RWY 22R. HAPPY THE CTLR CAUGHT IT. SUPPLEMENTAL INFO FROM ACN 551478: WE WERE READY AND CLRED. MAX TKOF PWR TKOF AND BEGAN ROLL. NO REMARKS BY TWR ABOUT ANY SHORT FINAL TFC TO ANY RWY. APPROX 90--100 KTS TWR WAS OVERHEARD SENDING AN ACR RJ AROUND; NO RWY INCLUDED. APCHING INTXN OF RWY 22R; FO LOOKED TO RWY 22R FINAL AND SAW AN ACR Y RJ ON GAR NOT WITHIN 500 FT CONTINUED TKOF WITHOUT INCIDENT. WE WERE NEVER GIVEN NOTICE BY TWR OF ANY TFC ON FINAL TO ANY RWY AT ANY TIME; ALSO WE NEVER RECEIVED ANY TCAS ALERT.