Just double checking that tie-breaker rules only come into effect if more than one parent tries to claim child.

Unmarried couple living together all year with 2 children. I do both returns. House is in his name only and he earns a little more so HOH goes to him. She files single claiming kids as dependents. This is the way the overall tax is the lowest.

I've done it this way in the past, but for some reason I'm second guessing myself.