There are two support rules that come into play.
First, for her to be your dependent, she must not have provided more than half her own support, for the whole year. For this rule, the support does not have to be from earned income (wages). But, be careful about what you are calling her own support. Scholarships don't count as her own support (they are totally ignored in the support calculation). 529 plans, where you are the owner and she is the beneficiary are not her own support. Loans totally in her name are her support (you are not a co-signer). While away at school she is still considered as residing with you. The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.
Second rule: An 18 year old (or a full time unmarried student, age 19-23), even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he supports himself by working (earned income). You cannot be supporting yourself on parental support, 529 plans, investments or student loans & grants.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. This is worth up to $2500 (AOTC shifts to all non refundable).
