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From reading the article, I think the point is that these kids aren't actually supporting themselves, they're just made to seem that way on paper.

Surely their income from their parents is taxable at normal income tax level then?

Only if they give/receive more than 11.1 million over the course of their lifetime.

And that, only the amount over $30k/yr for a couple gifting their child.

Alas there are some pretty generous tax breaks on gifts.