Assuming they otherwise qualify to be claimed as dependents, the right to claim the children goes to the custodial (as defined by the IRS) parent - the parent with whom the child(ren) spent the most nights during the tax year.
Also, if the custodial parent paid more than half the cost of keeping up a home for themselves and at least one of the children, that parent may file as Head of Household. This assumes the two spouses did not live together at any time during the last 6 months of the tax year.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
