If you are unmarried, and you have a child together who lives with you more than half the year, then either one of you could claim the child as a dependent, but only one of you can claim the child. If the parent who claims the child as a dependent is also the person who pays more than half the total household expenses, that parent can use head of household instead of single. The parent who does not claim the child as a dependent would file as single.
In that case, you leave the child off your return completely. Don't add their name and start answering questions about custody. That can lead to confusion and filing of incorrect or conflicted tax returns. The parent who will not claim the child should just leave that section blank.
