Somewhere on the tiny atoll of Fakaofo is the face that launched a tiny outboard-powered dinghy.

Three lovesick teenage boys rescued after 50 days adrift on the South Pacific have reached dry land, gaunt, ill, and lucky to be alive. Samuelu Peleha – also known as Sam Perez – and Filo Filo, both 15, and Etueni (or Edward) Nasau, 14, disappeared from Tokelau's Atafu Island on October 5 when they sailed off to a neighbouring atoll looking for love.

A search by a New Zealand Air Force Orion failed to find any trace, but on Wednesday, a New Zealand fishing boat spotted a tiny aluminium dinghy. The boys had stolen it to get to Fakaofo atoll after a girl had caught their eye at an island sports event that day.

They drifted 1300 kilometres off course and survived on a few coconuts and a seagull before the tuna boat San Nikunau picked them up. They arrived at the Fiji Navy base in Suva yesterday and had to be helped ashore.

They were all put on IV drips and one appeared to collapse into an ambulance before being taken to Suva's Colonial War Memorial Hospital, where they were under observation last night.

A New Zealand high commission spokeswoman, who met the boys off the boat at 3pm yesterday, said they did not say a word. "They were just really weak and they looked relieved to be on land."

Extended family members living in Suva visited the boys in hospital.

Locals said a sports competition was hosted by the boys' atoll, Atafu, in October. Among the visitors was a girl from neighbouring atoll Fakaofo, who captured the eye of one of the boys.

She sailed home after the tournament, and after midnight, emboldened by alcohol, they decided to take the island's newest small boat and visit her 200km to the south.

They had a couple of sacks of coconuts, some beer and a fuel tank.

Their cousin and Atafu representative, Kuresa Nasau, said nobody saw them go but it would not have been thought unusual. "Young kids go out fishing all the time, nobody questions that. They were seen at midnight and nobody suspected they were going to take off."

Tokelau – a nation of just 1200 people scattered across three atolls – is celebrating the rescue, but the three will face hard questions when they return.

San Nikunau first mate Tai Fredricsen, of the Bay of Islands, said it was a miracle the tuna boat found the boys."We saw a small vessel, a little speedboat on our bows, and we knew it was a little weird," he said.

The boys started waving so the boat pulled up beside them. "I ... asked them if they needed any help they said, `Very much so'. They were ecstatic to see us."

The boys were skinny but in good shape for the time they had been at sea. "Somehow they caught a bird, I don't know how, but they caught it. They ate it, that is what is recommended."

The boys had started drinking seawater a few days before the rescue and probably would have only survived for a few more days, Mr Fredricsen said.

Mr Nasau said he had heard about the late-night love quest and the boys would have questions to answer when they got back. "I heard there was some alcohol involved. I will investigate but all I was concerned about was their safety."

The boys will head to Samoa when they are well – hopefully tomorrow – to wait for the next boat home on December 16.