Is that kind of "old money" an increasing or decreasing phenomenon?

I don't have the numbers, but it seems like a lot of the rich people that come to mind made most of their money during their lifetime.

Also, wealth naturally dissipates pretty quickly over generations. One reason is simple fan out. Another reason is that the children are likely to be less frugal, and there's s high chance that some descendants are downright reckless financially.

Money doesn't have to be all that old. Trump, for example, is only second generation money. But still he inherited a couple of hundred million, and wouldn't be where he is now without his rich dad.

How long this wealth lingers van vary a lot. If it gets divided among multiple children, it dillutes pretty quickly, but those children are still far richer than average children. You need either many generations of dillution or some really terrible mismanagement to restore this aristocracy back to regular people. And all those generations in between do wield power and wealth they never earned.

Of course an economic revolution like the internet is giving us, creates a lot of new millionaires and billionaires, and if they let their children inherit their entire wealth, that would create a fresh new aristocracy. Though I'm glad to see that a lot of new billionaires put their money to more philantropic uses. Not all of them, though.