New Zealand

New Zealand was first settled by Polynesians between about 1280 and 1350. James Cook was the first European to land in 1769. Britain declared sovereignty in 1840, signing the Treaty of Waitangi with Maori chiefs, then establishing the Crown Colony of New Zealand in 1841 (Source: Wikipedia). 

In a 1788 proclamation, NSW Governor Arthur Phillip declared NSW to encompass "all the islands adjacent in the Pacific Ocean," causing New Zealand to become a de facto part of NSW. From this date, NSW attempted to exercise legal control over New Zealand, not necessarily to the satisfaction of the Colonial Secretary (in England) and without consultation with Maori chiefs. Ultimately the Treaty of Waitangi led to proclamation of British sovereignty over New Zealand, which came into effect on 1st July 1841.       https://www.nma.gov.au/defining-moments/resources/new-zealand-becomes-a-separate-colony

Organised British migration to New Zealand commenced in 1840. Prior to this, Europeans settled in New Zealand numbered in the hundreds. These included convicts escaped from NSW, whalers, sealers, sailors, missionaries and merchants.

The Encyclopedia of New Zealand provides excellent summaries of the various phases of immigration throughout the 19th century, into the 20th century: https://teara.govt.nz/en/history-of-immigration