What belongs to who when it comes to wealthy families?

Usually, financially stable parents who pay for their kids’ clothes, phones, cars, etc. will say, “I paid for it, so it belongs to me.” But in extremely wealthy families that are 3 or 4 generations deep with hundreds of millions or even billions of dollars, what actually belongs to who?

At that point, the money may not have originally come from the parents themselves — it could’ve been inherited from grandparents or great-grandparents and passed down through generations. So can parents in those families still say, “It’s my money because I paid for it,” when the wealth itself wasn’t originally theirs either?