Nope. For instance, amongst French oversreas territories, there’s a desert island mostly covered by water during high tides. And there has been an issue between two countries of the arabic gulf (can’t remember which ones, but one sent soldiers) some years ago about a minuscule island totally underwater during high tides.
When a volcanic island appeared in the mediterranean sea during the 19th century, Italy and the UK argued about possession of the volcano until it collapsed and sank again some months later.
Don’t forget that with any piece of land comes the much more important Exclusive Economical Zone, generally much more important than the island itself (even when the island is actually populated). So, nobody is going to forget about any piece of rock they could possibly put a claim on.
There is no land at the north pole. What land is near it is indeed claimed by various national and subnational entities (Canada, Russia, Greenland, and Norway). Much of Antarctica is also subject to territorial claims, though there are treaties governing its use.
Exile doesn’t always have to be “from the country”: after the Spanish Civil War of 1936-9, a relatively-common punishment was “exile to 100km” (I know people who got it for times between 1 and 10 years). It was used for people who were of a political bent that didn’t match the winners’, but who were considered “not dangerous so long as they’re not getting together with a bunch of their same-ideology buddies”; the distance was enough to put them into a different cultural zone altogether. In some cases, only the person who’d received the punishment would move, but more commonly the whole family would; after finding a home, job and friends in the new place, many of them didn’t go back once the exile was over.
If a new island appeared out of nowhere today, it would be interesting to see how it gets claimed. I don’t think being the first to throw down a flag will cut it anymore.
If you’re really including extra-terrestrial real estate in the scope of your question, then there’s going to be a hell of a lot of land that qualifies as “no-man’s”. In fact, pretty much all of it, to a good approximation.
Well, new islands HAVE appeared, such as Surtsey, and the more recent volcanic island off Tonga. Of course, new volcanic islands tend to be economically useless (except maybe for tourism) and difficult to inhabit, at least in the short term. It’s also likely they will be near existing land, so it’s clear who they belong to, and nobody wishes to argue about it, provided the owners cooperate with the scientific researchers who will be interested in studying them.
For the French one, you may be thinking of the Bassas Da India, a coral atoll in the Mozambique channel:
It’s main purpose seems to be to serve as a navigation hazard, accumulate shipwrecks, and provide wonderful wall dives for scuba divers. That doesn’t stop Madagascar and France from contesting ownership of it. At a few historical points, I believe there were suggestions from maritime interests that the damned thing be blown up to remove the hazard.
If you dig through the CIA World Factbook, and look under “international disputes”, you will discover that most major nations have some contested bits of real estate. Canada and the US, for instance, contest Machias Seal Island and nearby North Rock. “Hey, it’s part of Maine. It belongs to us.” … “No, it’s part of New Brunswick, and WE have a lighthouse on it.” … “You’re squatting. Besides, it’s a bird sanctuary.”