I can file Head of Household for my qualifying child whom I will NOT claim as a dependent. But I can't get TurboTax to that setting.

It's only letting me use as a qualifying child for EIC or dep care.  But not for HOH.  How do I get TurboTax to let me have HOH without a dependent.  She's 18 and will be claiming herself on her own tax return.

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If you do not have a qualifying person as a dependent on your tax return, you are not married and filing as Single then you cannot have Head of Household filing status.

See this TurboTax support FAQ for HOH - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539

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Why aren't you claiming her?  She is under 19 so you should be able to claim her no matter how much she made.  She can not claim herself.  Even if you (or her other parent) don't claim her she has to check the box on her return that says she can be claimed.