You can claim your student as your Dependent (unless they are over 24) and you provided over half their support. It doesn't matter how much they earned. Paying their own expenses with grant/loans/scholarships doesn't count as 'supporting yourself'. If they lived away from home while attending school, indicate that 'they lived with you all year'.
It doesn't matter who paid their Education Expenses, you or them. If you claim them as your dependent, you can claim their Education Expenses on your return.
Here's IRS Info on Education Tax Benefits.
@Pbellini
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