FLC OF B737 DSNDING IS ISSUED TFC ON CLBOUT. BOTH HAVE EACH OTHER IN SIGHT. CTLR THEN ISSUES A TURN WHICH PUTS THE TFC ALMOST OPPOSITE DIRECTION. TCASII ISSUES TA; THEN RA WHICH FLC FOLLOWS. NMAC.

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WHILE DSNDING INTO ITO; HI; WE WERE ORIGINALLY CLRED TO DSND FROM FL250 TO 17000 FT ON A 105 DEG VECTOR TO JOIN V15 NW OF ITO. DURING DSCNT; WE WERE POINTED OUT AS TFC TO AN OUTBOUND ACR FLT WHO CALLED US IN SIGHT. WE THEN HAD THE OUTBOUND TFC POINTED OUT TO US AND AFTER A FEW SECONDS RPTED HIM IN SIGHT. HE WAS AT OUR 1 O'CLOCK POS AND THE TCASII DISPLAY SHOWED HIM TO BE MORE THAN 20 MI DISTANT AND MORE THAN 4000 FT BELOW US; AND I BELIEVE CLBING. THE CTR CTLR THEN TURNED US R TO 110 DEGS; THEN CLRED US TO 9000 FT TO MAINTAIN VISUAL SEPARATION WITH THE TFC. THE TURN PUT THE TFC CLOSER TO OUR 12:30 O'CLOCK POS. FOR THE NEXT MIN OR MORE; I CONCENTRATED ON MAINTAINING VIGOROUS VISUAL CONTACT WITH THE TFC EXPECTING IT TO PASS TO OUR R SIDE AND ABOVE US ON ITS CLBOUT. IT WAS MY PERCEPTION THAT THE OTHER ACFT WAS ESSENTIALLY ON AN OPPOSITE PARALLEL COURSE BOUND FOR HNL AND WOULD BE CLBING AS WE DSNDED. SHORTLY THEREAFTER; WE RECEIVED A TCASII TA. UNDERSTANDING THAT I WAS BURDENED TO MAINTAIN VISUAL SEPARATION I EXECUTED A 10 DEG L TURN WITH THE AUTOPLT AND RAPIDLY INCREASED THE RATE OF DSCNT FROM ABOUT 2500 FPM TO ABOUT 4500 FPM ACCELERATING FROM 280 KTS TO ABOUT 345 KTS. THE OTHER ACFT INQUIRED OF CTR ABOUT OUR ACTIONS AND WAS RATHER MATTER OF FACTLY TOLD THAT WE WERE MAINTAINING VISUAL SEPARATION. SHORTLY THEREAFTER; WE RECEIVED A TCASII RA TO CLB. I DID NOT EXECUTE A CLB BECAUSE THE TFC WAS IN SIGHT AND WAS LESS THAN 1000 FT BELOW US. I DID NOT BELIEVE I COULD SAFELY REVERSE THE DSCNT IN TIME. I ALSO BELIEVE I WOULD HAVE LOST SIGHT OF THE TFC. I DID EXECUTE A 30 DEG BANK L TURN AND I BELIEVE THE OTHER ACFT TURNED L AS WELL. THE MAJOR CONTRIBUTING FACTOR IN THIS INCIDENT WAS ACCEPTING THE UNSOLICITED CLRNC TO MAINTAIN VISUAL SEPARATION ON CONVERGING TFC AT NIGHT; FOLLOWED CLOSELY BY MY INCORRECT ASSUMPTIONS ABOUT THE ROUTING OF THE OTHER ACFT WHICH WAS ON A SLIGHTLY CONVERGING COURSE AND APPARENTLY LEVELED AT 16000 FT ENRTE TO OGG. TCASII WAS INSTRUMENTAL IN ASSISTING BOTH CREWS TO MONITOR THIS SIT AS IT DEVELOPED BUT MAY HAVE LED TO A FALSE SENSE OF SECURITY WITH THE INFO PROVIDED EARLY ON. TCASII DID PROVIDE THE ULTIMATE WARNING TO PROVOKE EVASIVE ACTION. SUPPLEMENTAL INFO FROM ACN 385072: WE; ACR Y; WERE LEVEL AT 16000 FT ON OUR WAY TO MAUI FROM HILO. ATC ADVISED US OF TFC (BEYOND 12 MI) AT OUR 12 O'CLOCK HIGH. WE RPTED ACR X IN SIGHT. ACR X WAS TOLD ABOUT US AT HIS 12 O'CLOCK LOW; AND THEY RPTED US IN SIGHT. ACR X WAS GIVEN A DISCRETIONARY DSCNT THROUGH OUR ALT AND WAS TOLD TO MAINTAIN VISUAL ON US. ACR X DSNDED INTO US; 12 O'CLOCK; STOPPED AT 16000 FT; CAUSING US TO RECEIVE A FULL DOWN; COMPLETELY RED RA. ACR X THEN TURNED L; SO WE THEN TURNED L TO AVOID; NARROWLY MISSING ACR X AS THEY WENT BY OUR R SIDE. ATC RECONFIRMED THAT ACR X WAS TO MAINTAIN VISUAL FROM US. 2 MAJOR CONCERNS: 1) ATC USING VISUAL DSCNTS ON CONVERGING TFC; ALLOWING OR TRUSTING THE DSNDING TFC TO SHOW GOOD JUDGEMENT AS TO WHEN TO DSND. AND 2) THIS KEEPING 'IN SIGHT TFC' CLB/DSCNT CLRNC SHOULD NOT BE ALLOWED UNTIL TFC IS EITHER ABEAM OR BEHIND ONE ANOTHER. ACR X SHOWED POOR JUDGEMENT DSNDING 50+ MI OUT FROM ARPT; AND BEFORE CLRING US; DSNDING THROUGH OUR ALT.