Get your taxes done using TurboTax

HOH means one provided more than 50% of the support for the entire household for the ENTIRE YEAR. You meet that qualification for your household.

I assume BF does not have any of his own children living with him. Why does he think he qualifies for HOH? Did he live elsewhere prior to October?  You and your kids are not related to him, so cannot qualify him for HOH in any case.)