I have 2 children with a woman i never married. There is a custody agreement which she has "custody" and there's no regard to who can claim dependents on their taxes.

 My son lives with me 100% of the time, except for visits to her.  There is nothing in the custody agreement regarding dependent filing situations. I figured she could file and claim him because she has legal custody.  In such a situation can I claim head of household and use my son as the qualifying person?  If i can is there anything that i must document or send to the irs?