Everything you said is correct. The student is your dependent and a gift tax return (form 709) is not required.
A couple of side/back story issues:
1. Support doesn't matter, for dependency, if the student is full time and under age 24.
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit. They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
- He lived with the parent (including temporary absences such as away at school) for more than half the year
If your child is over 23, then the amount of support you provided does matter, for dependency. For gift tax return purposes, it is support, not a gift.
2. An unrestricted scholarship can be allocated anyway you want. Although not applicable, in you case, parents can allocate scholarship to non quailed expenses (room & board), on order to free up qualified expenses (tuition) to claim the education credit. In that case, the part of the scholarship used for non qualified expenses becomes taxable income, to the student (not the parent).
