If the mother and child live with the grandparent, then the grandparent can claim the child, if the mother is not claiming the child. The mother gets to say who can claim the child, either the grandparent or the father. The father gets no say. His support and weekend visits are irrelevant. Since the father is the non-custodial parent, he can only claim the child if the custodial parent (the mother) gives him permission, on IRS form 8332.
The grandparent does not need form 8332 because he/she also lives with the child. The child is the "Qualifying Child" of any related taxpayer in the household (either the mother or grandparent).
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
.A child closely related to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support
- He lived with the relative (including temporary absences) for more than half the year
- He is younger than the relative (not applicable for a disabled child)
- If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
- If the parent of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
