Wellington Coroner Richard McElrea has begun an inquiry into the deaths of Indonesian crew members Samsuri, 39, Taefur, 35, (SUBS: BOTH HAD ONLY ONE NAME) and Heru Yuniarto, 25.
Pathologist reports said they had drowned.
The bodies of the Korean captain, Shin Hyeon Gi, 42, and two other Indonesians have not been recovered and their deaths are not subject to this week's inquest.
At the outset, Mr McElrea formally expressed his condolences to the families of the dead.
The inquest, expected to last all week, was scheduled to follow the findings of a ministerial inquiry into the fate of the trawler.
A Transport Accident Investigation Commission probe was also held into the vessel's sinking.
The coroner said he would not deal with the wider issues of working conditions on board, except where they related to circumstances relevant to the inquest.