Tax question: Should high income parents claim their college student child as a dependent?

I though when figuring out support, all scholarships were excluded, as well as the tuition and other expenses they pay. For example, if student’s tuition was $30k and scholarship was $30k, that figure is just left out. Parent didn’t pay, student doesn’t get credit or dinged for that, it just isn’t there. If student also got $15k for r&b, that’s out too. So, what is the cost of this students living expenses for the year? It may only be a few thousand dollars - summer rooming, cell phone, car insuranc3. The question then becomes who paid more than half of those, as small as they might be?