The IRS goes by physical custody of a dependent child, so if the child lives in your home over 183 nights of the year then you are the custodial parent.
If someone claims a child on their tax return and the tax return has been filed and accepted by the IRS, then you will not be able to e-file your tax return. You would need to print and mail the tax return and claim the child on your return. If you have a tax refund the IRS will pay the refund.
Within a year the IRS will contact both parties by mail requesting that they amend their tax return if they were not eligible to claim the child as a dependent on their tax return. If the IRS does not receive an amended return then they will contact both parties again requiring proof that the child was eligible to be claimed on the tax return. The losing party gets to pay back any refund based on the child being a dependent plus penalties and interest.
