Just think how close they were to being a part of that new island. Suppose the eruption was just below them when it occured. I wonder if they realize how close they were to a disaster?
I believe they can (claim it) only if it is in international waters. You can establish your own country that way. Otherwise, it will be the property of the existing country if it is within their territory. Just from what I read...which is minimal.
Hawaiii is continuously forming new islands (or addition to existing ones)...might take millions or billions of years but they slowly but surely building several of them...made of lava too! [:0]