Although Maui fished up the North and South Islands, it was the great Polynesian navigator Kupe who discovered them. Kupe lived in Hawaiiki, mythical ancestral homeland of the Māori. In Hawaiiki a canoe maker by the name of Toto also lived.
Toto fabricated two huge ocean going canoes from a large tree. One canoe he named Aotea and the other he named Matahorua. Toto gave his canoe named Aotea to one of his daughters, Rongorongo, and the other canoe named Matahorua to his other daughter, Kura. It happened that Kupe desired Kura very much. However, Kura was already the wife of Kupe's cousin Hoturapa.
When Hoturapa and Kupe were out fishing one day, Kupe ordered Hoturapa to dive down and free Kupe's fishing line, which had become tangled. When Hoturapa dived into the sea to free the tangled line, Kupe sliced through the anchor rope of the canoe, and began to row furiously back to shore. Hoturapa drowned, but his family were suspicious of the circumstances surrounding his death. It was, in fact, a plan on Kupe's part to take Hoturapa's wife Kura.
In order to avoid vengeance from Hoturapa's family, Kupe and his own family left Hawaiiki in Kura's canoe Matahorua. After some time of navigating, Kupe's wife Hine Te Aparangi sighted the islands of New Zealand, which appeared as land lying beneath a cloud. Because of this, they named the islands Aotearoa, Land of the Long White Cloud.
As Kupe and his crew were sailing along the coast of this new land, they disturbed a giant octopus, who was hiding in a coastal cave. Terrified at the sight of a strange canoe filled with human beings, the huge octopus swam rapidly in front of the Matahorua and took flight, passing through the strait between the North and South Islands. Kupe followed the octopus, and discovered modern Cook Strait.
Kupe and the Matahorua eventually caught up with the giant octopus. In defence, the octopus whipped its enormous tentacles around the canoe, intent on devouring the whole canoe. During the furious battle which followed with the sea monster, it became obvious that the Matahorua was in great danger of breaking up.
However, Kupe suddenly had an idea, and threw a large water gourd overboard. The octopus, thinking that a man had fallen over, released it's tentacles from the Matahorua and turned to attack the gourd. Kupe seized this opportunity, and waited until the octopus was entwined around the gourd. Kupe then attacked the head of the octopus with his adze, and the octopus died. (Whitmore)
The great battle between Kupe, his warriors, and the giant wheke (octopus) of Muturangi took place at the top of the South Island. Kupe's children, wife, and other whānau members stayed at Te Whanganui-a-Tara (Wellington), to gather supplies and to keep safe from what Kupe knew would be a fierce sea battle.
The other version of the story differs from the original somewhat. Here there is no murder involved and the villain is a giant cuttlefish.
As the story begins Kupe and his friend Ngake were living in Raratonga due to a quarrel in their native Tahiti. The chief of Raratonga, Muturangi, had a pet cuttlefish known as Whekeamuturangi. Whenever Kupe or his friends went fishing they nerver caught any because the cuttlefish stole the bait from their fishhooks. They suspected that the cuttlefish was doing this at the behest of Muturangi.
Kupe and Ngake fashioned two canoes so they could go out and slay Whekeamuturangi.
Muturangi must have warned the cuttlefish, because he fled into the deep ocean. Ngake followed him immediately. Kupe stayed behind to collect provisions before following Ngake.
His wife Hine Te Aparangi and their five children accompanied Kupe on this voyage and eventually they overtook Ngake.
The two canoes chased the cuttlefish until it took refuge in a cave near Castle Point, then known as Rangiwhakaoma.
Kupe and Ngape abandoned their pursuit of the cuttlefish for a while and explored the area of Te Whanganui o Tara. According to the story what is now knows as Wellington Harbour was a freshwater lake. Both explorers tried to force their way through. Ngaka tried but only managed to create Lyall Bay but Kupe succeeded thus forming the present entrance to the harbour.
Returning to Te Rimurapa they saw the cuttlefish and gave chase. This time Kupe and his followers were victorious and the cuttlefish was slain
Somewhere in this story Kupe left his two daughters, Mohuia and another behind near the Cook Straight. After being gone a long time they presumed that he was dead.
They mourned for him and according to tradition lacerated themselves with shells so that their blood flowed over the rocks.