That could be complicated. For a child under age 19 as of December 31 (or a child who is any age and disabled), their parents can generally claim them if they "live at home" more than half the year. It does not matter who pays their living expenses. Being "away" at college or a boarding school is usually considered a temporary absence and the child is still considered to live at home for the dependent test. However, if this a permanent arrangement, then the child is not temporarily away from home and does not live with you. If the child does not live with you, you can only claim them if you pay more than half their living expenses.
There is an IRS web page that will walk you through some questions, and the rules are here as well.
https://www.irs.gov/forms-pubs/about-publication-501
https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent