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Ronan Hughes (40) became the second man to plead guilty over a case that shocked Britain and Vietnam and shone a light on the illicit human smuggling trade.
The other is Maurice Robinson, from the British province of Northern Ireland, who was driving the truck when the bodies were found.
Appearing at a full Old Bailey courtroom in London on Friday, Hughes stood in the dock facing the judge as the names of the 31 men and boys and eight women were read out.
He admitted each charge in a process that took more than 10 minutes.
Hughes also admitted conspiring to assist unlawful immigration.
Most of those who died, aged between 44 and 15, were from Nghe An and Ha Tinh provinces in north-central Vietnam, where poor job prospects, environmental disasters and the promise of financial reward abroad fuel migration.
They were discovered in October last year in a container at the back of a truck on an industrial estate in Grays in Essex, about 30km east of London.
A third man, Eamonn Harrison (23), also from Northern Ireland, pleaded not guilty to the same charges.
A trial is due to begin on October 5.