CONFLICT OCCURS WHEN MLG IS TOLD TO MAINTAIN VISUAL SEPARATION FROM AN MD80 ON DEP FROM LAX.

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WE WERE CLRED FOR TKOF ON RWY 24L HDG 250 DEGS; MAINTAIN VISUAL SEPARATION WITH MD80 ROLLING ON RWY 24R. TWR'S INSTRUCTIONS INCLUDED; 'HE'S TURNING NBOUND.' BELIEVING THE MD80 WOULD BE TURNING TO THE N JUST AFTER TKOF; WE BEGAN OUR TKOF ROLL. WE WERE BEHIND MD80 AS WE STARTED OUR TKOF; BUT WHEN WE BECAME AIRBORNE WE BEGAN TO OVERTAKE THEM. THE MD80 HAD NOT TURNED AND CONTINUED TO PARALLEL OUR COURSE; TRAILING 1000 FT BEHIND US. I INFORMED THE TWR OF THIS BUT GOT NO RESPONSE. MD80 XMITTED TO US THAT THEY HAD US IN SIGHT. I BECAME CONCERNED ABOUT THE CONTINUED SAFETY OF THIS OP SO WE LEVELED OFF AT 2000 FT (WE WERE CLRED TO 3000 FT). THE MD80 HAD CLBED TO 3000 FT; AND WAS STILL PARALLELING OUR COURSE. THE MD80 REQUESTED A TURN TO THE R AND WAS FINALLY GIVEN ONE BY DEP. WE RPTED LEVEL AT 2000 FT TO DEP AND WHEN WE SAW MD80 FINALLY BEGIN TURNING AWAY; BEGAN CLBING TO OUR NEWLY ASSIGNED ALT OF 13000 FT. ATC PROVIDED NO HELP TO EITHER ACFT DESPITE REPEATED CALLS DUE TO FREQ CONGESTION IN AN EXTREMELY BUSY TERMINAL ENVIRONMENT. WE HAVE GROWN SO USED TO OPERATING IN CLOSE PROX TO OTHER ACFT ON PARALLEL RWYS; PARTICULARLY ON RWYS 1 IN SFO THAT WE CAN BE LULLED INTO ACCEPTING A POORLY PLANNED CLRNC SUCH AS THIS ONE. HAD I KNOWN THAT THE OTHER ACFT WAS IN FACT NOT GOING TO TURN AWAY JUST AFTER LIFTOFF AS I HAD BEEN LED TO BELIEVE; I WOULD NEVER HAVE ACCEPTED THAT CLRNC. IT MUST BE REMEMBERED ANY TIME VISUAL SEPARATION IS ACCEPTED PLTS MUST HAVE AN OUT TO MAINTAIN CTL OF THE SIT IF IT DOESN'T WORK OUT AS EXPECTED.