Her mother didn’t want to claim her anyway. Does that change anything?
Read the publication. Basically, if your child lived in your household for more than 182 nights of the tax year, then you are what the IRS defines as the "custodial parent" and no special or additional paperwork is needed.
Ok thanks. I didnt mention that the child is not biologically mine, but I didn’t see anything about that in the publication. Do I still have the right to claim her?
If not your legal child through other means (such as adoption) the only issue would arise if the child's real father wanted to claim them and had legal right to do so either through the IRS rules, or if a lower court ordered the biological mom to sign the 8832.
wait a minute. If the child is not legally adopted by you or blood related to you, then the child would have had to live in your household for the "entire" year - not just half. So if they didn't live with you the entire year, you can't claim them at all.