AN NMAC DURING SIMULTANEOUS APCHS INTO LAX. MULTIPLE RWY OP PARALLEL APCHS.

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ON THE CIVET ARR FOR RWY 25L AND WAS GIVEN NUMEROUS SPD RESTRS. AFTER BREMER WAS CLRED THE VISUAL TO RWY 25L BEHIND PRECEDING TFC AND ASKED TO SLOW TO 140 KTS OR LESS. SPACING ON ACFT ONLY AROUND 2 MI. NUMEROUS TFC PRECEDING TO RWY 24R&L. FROM HUNDA INBOUND A TA OF ANOTHER ACFT ON SCREEN ABOVE US WITH HORIZ SEPARATION VARYING BTWN 400-100 FT. CAPT (PNF) ASKED SOCAL APCH ABOUT TFC NUMEROUS TIMES WITH SOCAL STATING TFC IS FOLLOWING FOR RWY 25R. OUR QUESTION: FOLLOWING WHO AND DOES HE KNOW WHAT ACFT TO FOLLOW? JUST PRIOR TO LIMMA; RECEIVED AN RA TO DSND AND FOLLOWED MANEUVER WHICH PUT ACFT BELOW APCH PATH. PNF/PF STILL COULD NOT SEE ACFT ON RWY 25R SO REQUESTED A L TURN FOR MANEUVERING AND WAS NOW TOLD BY TWR THAT HAWTHORNE WAS OFF OUR L WITH NUMEROUS TARGETS AND AT OUR ALT HE COULDN'T GUARANTEE SEPARATION. TWR ASKED IF WE STILL COULD SEE RWY AT WHICH TIME WE FINALLY SAW THE BRASILIA JUST OFF OUR R WING ON RWY 25R. WE WENT AHEAD AND LANDED RWY 25L WITHOUT INCIDENT. BOTH ACFT TOUCHED DOWN AT THE SAME TIME ON RWYS 25L AND R. SIT WAS ONE IN WHICH THE DENSITY OF TFC TO PARALLEL RWYS WITH VISIBILITY DUE TO HAZE AND SUN AT VMC MINIMUMS. SUGGEST CTLRS AS WELL AS PLTS OF COMMUTERS. RECEIVE TRAINING ON TCASII AND ITS INHERENT ABILITY TO MAINTAIN FLT PROX TO OTHER ACFT AT A MINIMUM. IF THAT PROTECTED AIRSPACE IS VIOLATED; WE MUST MANEUVER WHICH IN THIS CASE LEFT US WITHOUT A SAFE OPTION.