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I am in a similar situation.  I was never married to my ex but had two children with her.  She does not work and is on ssdi.  She files no taxes.  She rents off from her parents and allows her parents to claim the children.  I pay support and take the children biweekly.  I feel I am entitled to claim them as they are my biological children, their mother can not claim them and I pay support.  They do not live with me full time. However I meet all the other qualifying tie breaker rules.  Looking forward to a reply! Thank you for your help.