The custodial parent is the one with whom she lived with the most nights and time away at school counts as time with the parent. If she spends more nights with you during the year than with father, you are the custodial parent. In that case he cannot file as head of household even if you give him permission via a signed form 8332 to claim her. Even if he claims her, you as custodial parent can still file as head of household if you are otherwise qualified.