ACR X TCASII RA AFTER TKOF WITH SMA Y IN HNL ATA TCA. MULTIPLE RWY OP INTERSECTING RWYS.

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ACR X DEPARTED 8L NORMALLY; BEGINNING A R TURN AT 200 FT EBOUND. AT APPROX 600 FT THE TCASII GAVE A TA FOR TFC AT OUR ALT; CLBING; SO CLOSE THAT I (PNF) CHANGED RANGE TO SEE IF I WAS ON 12 MI BY MISTAKE. WENT BACK TO 6 MI RANGE; SAW TFC R ON OUR IMAGE; LOOKED OUT AND SAW SMA Y CLOSING WBOUND JUST BELOW US AT ABOUT 1/2 MI RANGE. TWR SWITCHED US JUST THEN. I MADE FREQ CHANGE AND CALLED DEP AS I CALLED TFC IN SIGHT TO THE FO (PF). SIMULTANEOUSLY; TCASII GAVE RA WITH RED BAND COVERING WHOLE VERT SPD RANGE EXCEPT 4-6000 FPM CLB. SLATS RETRACTED AS FO ALSO SAW TFC NOW TURNING AWAY FROM US; JUST BELOW OUR ALT. ONCE CLR OF TFC WE ASKED DEP WHO THE TFC WAS. SHE SAID HE WAS TALKING TO THE TWR. WE COMMENTED IT HAD BEEN MUCH TOO CLOSE FOR US; AND TO PLEASE PASS IT ON TO TWR. CLRLY THIS WAS TFC THAT SHOULD HAVE BEEN POINTED OUT TO US; IF INDEED WE SHOULD HAVE EVEN BEEN CLRED FOR TKOF WITH THE SMA ON ITS WBOUND; CLOSE-IN (TO RWYS) FLT PATH. AS WE WERE IN A TURN TAKING US AWAY FROM THE SMA ANYWAY; NO IMMEDIATE EVASIVE ACTION WAS REQUIRED BY OUR ACFT; BUT THE SMA DID TURN AWAY. THE DEP CTLR SHOWED NO EVIDENT CONCERN SINCE THE SMA WAS IN TWR'S AIRSPACE. WE WERE CONCERNED! A CONTRIBUTING FACTOR MAY HAVE BEEN THAT TWR HAD TAKEN TOO MUCH ON IN TERMS OF MOVING ACFT AND LOST SIGHT OF POSSIBLE DEP CONFLICTS. SHE HAD SLOWED AND WIDENED OUT OUR COMPANY ON A BASE APCH TO MAKE AT SLOT FOR OUR TKOF AND TOLD US TO DEPART WITHOUT DELAY AS WE TAXIED TOWARD THE APCH END. THIS IS THE FOURTH TIME IN 5 WKS I HAVE PERSONALLY BEEN INVOLVED IN A NEAR TFC CONFLICT ON TKOF OR APCH; BELOW 800 FT; WITH NO TA FROM THE TWR.