Deductions & credits

Thanks.  One of the TTax help pop-ups discusses the situation of unmarried parents who are living together.  In this case TTax says "If you're living with the other parent and aren't married and don't have an agreement,
the parent who has the highest adjusted income for the year has the right to claim the child on their tax return. " I'm somewhat unclear regarding what "has the right" means.  In my daughter's case they are not living together and don't have any sort of formal agreement regarding custody, or support for that matter.  It is the case that my daughter provides virtually all the financial support for this new child.  My daughter works and has independent health insurance, etc.   The TTax help in this case seems to assume that the parent with the highest adjusted income would benefit most from the dependent deduction -- but this also seems to assume that that parent would also be contributing significantly to the household where the new dependent actually lives.  It's also the case that (1) both my daughter and her baby's father have other dependent children from prior marriages (so both have filed as heads of households and have custody agreements with their respective ex-spouses_) and (2) reside in different states.  My daughter plans on claiming the new child as a dependent.