The following is a composite of much Polynesian folklore related to "the-place-from-where-we-all-came":
A very long time ago the great sea was not so deep, and the land was mostly on two very big islands, like two giant turtles floating in the water. One of these was high up on the earth's shoulders, in cold water. No one cared to make a home on that shell. Only wild beasts, and maybe some bad Menehune, lived there. The other island basked in the warmth of the sun at the belt of the earth. In their old way of speaking, the people who lived on this shell called it aina-momomaakane, fat-land-of-god. For them, everything was good, and everyone was happy. There was little need for work, and mostly people could just do as they pleased, with no one or nothing to bother them.
Then everything changed. Some say the old ways were brought to an end because a man and a woman desecrated the flower garden of a god, and everyone was to be banished to a small floating land, where their descendants were to be doomed to scrape food from rocks. But there is another story. One which tells of an unusually cold morning when much dew appeared on all the plants. The earth slipped on a wet hibiscus, and fell onto its back. The great white giant who slept in the shadows at the top of the world woke up and found himself under the rays of the hot sun. To hide again, he quickly changed into water. Other gods, the red ones, Pele's ancestors, roared in anger at being disturbed. All of this made a great commotion.
When everything finally settled down, the people found there were very few of them left, and they were no longer living on a great turtle-back, but on the scattered fragments of one, that is to say, on many, many small islands. And the stars above them in the night sky were now those which before could only be seen much farther south of the belt of the earth. (Those many small islands today have names like Fiji, Tonga, Samoa, and Tahiti.)
But the sea was not totally malevolent: to help the people after the big shake-up, everything beneath the waters grew back faster and bigger. To find each other, and try to learn what was left of their earlier homeland, the people built strong canoes from big trees that floated everywhere around the islands at the time. They soon found that the sea was giving them another present: thousands of small coral islets sprang up everywhere, like long strings of pearls, marking trails from one group of islands to another. Following one of these, they re-discovered far south a big chunk of their old place, named ka-paia-ha'a back then, later Aotearoa ("Land of the long white cloud"), and finally, New Zealand.
Going all over like this, in every direction, over many, many generations, they re-kindled life in much of the remnants of what had been their homeland.
Eventually, many of the coral islets died, and the sea rose more. The string-of-pearl trails between the island groups vanished. By then, there was no longer anyone still interested in finding pieces of the old ancestral home, and the diverse islander families found it too hard to keep in touch with obscure relatives in far-off places.
So, all moving ended. But not before, going along one last string-of-pearls-path north, the people found some of the big turtle-island that had lain in the north. The one which the ancient stories say was so barren, because it was in the wrong place, in cold water. It also had disappeared, the day the earth slipped, but several pieces of it had now been blown back out of the sea, in a much more pleasant location. So the people settled there also. And, because it reminded them so much of their old home, this last pearl they called Hawaii.