ACR X HAD LTSS FROM ACR Y. SYS ERROR.

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THIS EVENT INVOLVED 2 ACFT IN OCEANIC NON-RADAR AIRSPACE. #1 ACFT WAS ACR X (RNAV) 2000N/6000W DCT TOOMS. ALREADY ACTIVE AND IN MY SECTOR AT FL310 WHEN I ASSUMED SECTOR RESPONSIBILITY. #2 ACFT WAS ACR Y A SAN JUAN DEP VERMO DCT KRAFT. I AUTHORIZED ACR Y TO CLB TO FL280 WHILE I CHKED XING TIMES WITH ACR X AT FL310. SECTORS 2;4;6 WERE COMBINED AT MY POS AND IT WAS VERY BUSY. I COMPUTED XING TIME BASED ON A HANDWRITTEN BDY ESTIMATE IN BLOCK 21 OF FAA 7230.19. INITIALLY MY COMPUTATIONS INDICATED AN AMPLE 22 MIN. I THEN CLRED ACR Y TO FL310. I WAS THEN RELIEVED FOR A BREAK. IN THE PROCESS OF GOING BACK TO RESUME THE SECTOR (WELL AFTER THE ACTUAL XING) THE ADJACENT FACILITY SECTOR CTLR CALLED TO QUESTION THE XING TIME. WE THEN RECHKED THE ACTUAL PROGRESS OVER TOOMS AND FOUND THAT THE BDY ESTIMATE IN BLOCK 21 WAS IN ERROR. THE ORIGIN OF THIS ESTIMATE IS NOT KNOWN TO ME. WHEN I ORIGINALLY COMPUTED XING TIMES THE SECTOR WAS VERY BUSY; I DID NOT HAVE TIME TO DOUBLECHK THAT ESTIMATE. THIS CAUSED THE ACFT INVOLVED TO CROSS WITHIN 5 TO 7 MINS OF EACH OTHER. AT THE POINT OF XING BOTH ACR X AND ACR Y WERE OFF RADAR. ACR X WAS NEVER IN RADIO COM WITH US. IN ADDITION TO THE ALREADY HVY WORKLOAD; THE FACILITY WAS EXPERIENCING LANDLINE PROBLEMS THAT HAD ELIMINATED COM AND COORD WITH 3 ADJACENT ARTCC'S AND 3 APCH CTLS. I BELIEVE THE SECTORS BEING COMBINED AT A TIME WHEN IT IS FREQUENTLY SPLIT; PLUS LANDLINE COMS FAILURE WITH ADJACENT FACILITIES; AND THE ERRONEOUS BOUNDARY ESTIMATE (POSSIBLY WRITTEN BY A PREVIOUS CTLR) ADDED UP TO A WORKLOAD CONDITION IN WHICH I WAS UNABLE TO VERIFY AND DOUBLECHK.