AN A320 CAPT DIVERTS TO MMCU; CHIHUAHUA; MEXICO WHEN THE #2 ENG LOSES ITS OIL QUANTITY. THE FLT HAD LOST 2-WAY COM VIA ACARS WITH DISPATCH AND MAINT; BEING ABLE TO SEND BUT NOT RECEIVE MESSAGES.

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I TOOK OVER DISPATCH SECTOR AND WAS RESPONSIBLE FOR ACR AIRLINES FLT MEX-SFO. NO SIGNIFICANT WX ENRTE. AT AB38Z I GOT ACARS MESSAGE FROM FLT SAYING ENG #2 OIL QUANTITY WENT TO ZERO AND THEY TRIED/SENT 2 MESSAGES TO SFO MAINT. I CALLED MAINT AND THEY CONFIRMED RECEIVING MESSAGES FROM ACFT BUT WERE UNABLE TO SEND MESSAGES. APPROX AB40Z I GOT ACARS MESSAGE SAYING FLT WILL DIVERT TO CUU. AT AB43Z I SENT A SERIES OF ACARS MESSAGES TO ACFT VIA COMMERCIAL RADIO AND SITA; ASKING TO CONFIRM DIVERT; AND IF #2 ENG WAS SHUT DOWN. PER COMPANY PROC; I CONTACTED OUR MEXICO OPS OFFICE TO ARRANGE HANDLING AT CUU. I QUICKLY CHKED WX/NOTAMS AT CUU; NO PROB; VFR. AND AT AC16Z SENT MESSAGE TO TWR TO CONFIRM ON/IN TIMES OF AC00/AC05. ACFT MADE UNEVENTFUL LNDG. AS I SEE IT; THE PROB FROM THE DISPATCHER'S STANDPOINT; WAS LOSS OF RELIABLE COM BTWN DISPATCHER AND CAPT. I HAD TO PROCEED ON BASIS OF A CRYPTIC ACARS MESSAGE. AT THIS TIME; DAY; AND POS; THERE WAS A DEAD SPOT. SATELLITE COM OR HF RADIO WOULD HAVE BEEN A NICE BACKUP. AS IT WAS; I PROCEEDED WITH ASSUMPTION OF DIVERSION TO CUU; AND STARTED PROCESS OF NOTIFICATION OF DISPATCH MGR; AND PEOPLE HERE; VERIFIED WX WAS NO FACTOR; AND INITIATED HANDLING AT CUU THROUGH OUR MEXICO OPS.