Can two roomates both claim head of household for taxes both persons also ihave one child each. And pay for everything 50 -50 rent utilities

Not really.

If they EACH have a child, then, yes, they can each legally claim Head of Household (HoH).

However, the rules also require that the person claiming HoH provide MORE than half of the cost of maintaining a household for the child. This being the case, it is impossible for BOTH roommates to provide MORE than half of the cost of the household.

If both roommates DO claim HoH, it is likely the IRS will home in on the fact that they both claimed that status from the same mailing address, audit both roommates and essentially tell them to decide which of them is going to file as SINGLE vice HoH.