Simple answer: the parent.
If the student is your dependent, you claim the tuition credit.
If the student has taxable scholarship (box 5 of the 1098-T exceeds box 1), he reports that income on his return.
There are situations where both the student and the parent use the 1098-T.
The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income.
If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)
You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. In the 1098-T screen, click on the link "What if this is not what I paid the school" underneath box 1.
