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@jesusbowls wrote:

but what would ever be a reason to list a dependent as code Q

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The child lives with you (the custodial parent).  But you've given the 'ex' (the noncustodial parent who does not live with you) a Form 8332 to claim the dependency.

In the scenario, the 'ex' can only claim the exemption and the Child Tax Credit.  The Custodial Parent (claiming the kids with "Q") can potentially claim the Dependent Care Credit, EIC and Head of Household.