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@abs96 wrote:

 In this case can the dependent be claimed on the mother's return when he earned $37,000 versus his mother who earned $42,000 before expenses (self employed).

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Income has nothing to do with it.

Did the child pay for over half of his own support?  When you find that out, that is your answer.

https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf