New Holland was the name given to what is now Australia by the Dutch who discovered the continent in the first decade of the seventeenth century and charted increasing lengths of the northern, western and southern coasts during the next half century. The discovery and charting of the southern coast of Tasmania in 1642 settled any arguments that the landmass was part of a super-continent to the south or east.
A Dutch map of the Indian Ocean, made in the 1650s, includes almost all of the coast of Australia from the western entrance to Torres Strait to South Australia. And (separately) the southern part of Tasmania (which was assumed to be attached to the continent.)
James Cook discovered and charted the east coast in 1770 from about the New South Wales/Victoria border to Torres Strait and claimed this tract for Britain as “New South Wales” however, west of a rather mandatory line, the rest remained New Holland, at least for a few decades. (The British tended to refer to the continent as “Terra Australis” (South Land) but it was becoming less and less “Terra Australis Incognito”, its ancient sobriquet.)
During 1801/2 the great Matthew Flinders painstakingly circumnavigated the continental mainland. (He had already delved into Tasmania.) His account, published too many years later, includes the phrase: "Had I permitted myself any innovation upon the original term, it would have been to convert it into Australia; as being more agreeable to the ear, and as an assimilation to the names of the other great portions of the earth.”
Even without Flinders’ comment, New Holland’s days were numbered as the British moved westward. When the British flag was raised in Sydney Cove in January 1788 all of the continent east of a line drawn at longitude 135 degrees east was claimed - somewhat less than half of the landmass. New South Wales was to further encroach on New Holland in 1825 when the border was moved westward to 129 degrees east (over half way across the continent) to include a new (ultimately unsuccessful) British settlement on Melville Island, north of present Darwin. Two years after the settlement of Perth in 1829, the new colony of Western Australia was proclaimed and New Holland was gone.