Based on what you provided, it seems you don't meet one test for head of household and it isn't the support test.
1) the dependent must be your qualifying child which your BF isn't or
2) your BF must be a qualifying relative (QR) but for HOH purposes the following type of QR doesn't count
a) a person who is a QR only because he was a member of your household for the entire year
2) is the long way of saying to be a dependent for HOH purposes he must be related to you which he isn't.
