What is a continent? Europe, Asia, Africa, North America, South America, Australia and Antarctica are the usually listed suspects. But then Australia is sometimes referred to as an/the 'island' continent, implying that it somehow doesn't count. Presumably because it's smaller. Which would imply that New Zealand (for example) would have no chance of qualifying. But why should size matter? Short answer: it doesn't.
You may be used to thinking of the Earth as a ball of hard stuff, such as rock. But that is only because you are crawling around on the outside of it. The Earth is a hot and heavy ball, covered in a layer of hot liquid, covered in a thick layer of swirling gloopy hot toothpaste. The heat is what keeps the gloop in motion, creating ever-changing convection currents. On the outside, where it is coldest, the gloop acquires a thin frozen crust, which the currents soon drag back into the heat, where it melts.
Floating on the gloop there are frozen chunks of lighter stuff. It can sometimes get dragged down into the swirling gloop when it has got stuck to a bit of the crust, but even if it then gets melted it soon bobs back up to the surface. This lighter stuff is mainly granite, and the chunks are the continents.
So to tell if something is a continent, you need to ask two questions: is it mainly made of lighter granitic rocks, and if yes, is it currently attached to a bigger chunk of such rock? If the answer to the first is yes, then it is at least a part of a continent, and if the answer to the second is no, then it is the whole of the continent.
So, back to New Zealand (for example). Light granitic rocks? Check. Joined to something bigger? Not visibly. But if you look more carefully, in particular, if you look at the bed of the Pacific Ocean surrounding New Zealand, it turns out that New Zealand is essentially a range of mountains on a large chunk of continental rock, much of which is about two kilometres under water. Other parts of it that rise above sea level are New Caledonia, about a thousand miles to the north of North Island, and the Chatham Islands, around eight hundred kilometres east of South Island. This chunk of continental rock is not stuck to any other such chunk, and is therefore a continent. It is called Zealandia.
Zealandia used to be a part of Gondwana, attached to what would later become Australia and Antarctica. It broke off around 85 million years ago. In the process of breaking off it got stretched, which made it thinner. Being thinner, it does not float so high. There was probably very little land above water until around 25 million years ago, when the mountains of New Zealand started to grow.
Zealandia is around half the size of Australia. This is not just a useful fact with which to dazzle people at parties: Article 76 of the United Nations Convention on the Law of the Sea assigns sovereignty and undersea mineral rights partly on the basis of the extent of the continental shelf adjacent to a State Party's land territory. So it should come as no surprise that the Government of New Zealand spent tens of millions of dollars on a detailed geological survey of the extent of the sunken continent of Zealandia, establishing that 96% of its sovereign territory is under water.
More Interesting stuff
Zealandia and Article 76
Fun exercise in paleocartography (scroll down to December 6)