No. Neither one of them is related to you, so they cannot be qualified dependents for you to file Head of Household. If they lived with you for the whole year, and GF had less than $4400 of income you may be able to claim them for the $500 credit for other dependents. You do not get child tax credit or earned income for GF's child.
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.
https://ttlc.intuit.com/questions/4499708-what-is-the-500-credit-for-other-dependents-family-tax-cre...
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
