Ok I have step children. My partner claims them. But I do pay half. Can I claim head of house hold or say I take care of someone?

[Opus 17]

Your question is unclear.  Stepchildren means you are married to other parent.  In that case you can't file head of household.  You would normally file a joint return, if you file separate returns, either parent can claim the children but not both, stepchildren are legally the child of either parent for tax purposes.

Or, you are not married and these children are not yours legally or biologically.  In that case you can't claim them if the other parent files a tax return, and you can't use them for head of household if they are not your legal children by marriage or by blood.