Separated with child claiming head of household

I'm recently separated (never married) and will be claiming my daughter this year where my ex partner will claim her next year. If I file "head of household" will this have any impact on my ex partners return? The question on TurboTax has the answer "No, someone else paid more than half the cost", but technically it was split evenly where no one else paid more than half the cost. I'd like to ensure me filing head of household (as I'm claiming my daughter this year) will not impact my ex partners taxes this year.