Do I need form 8332 if unmarried, living together, claiming HoH, and letting the other parent claim the children?

My children's father and I have lived together all year with our two children. We split the rent. I pay all utilities and groceries: making me HoH. If we split the child benefits by him claiming them (child credits)and me filing HoH (higher deduction and EITC), will I need to include a form 8332? 


Everything I read is for custodial parent vs non custodial. We were never married, simply live together as coparents. So the term custodial does not really fit the situation.