Court custody of 50/50...court order does not specify what parent claims him for taxes....who gets to claim the child?

For tax purposes, the custodial parent is the parent normally allowed to claim the child as a dependent. A "custodial parent" here is the parent whose home the child spent the most nights in during the course of a year. If a child spent an equal number of nights in both parents homes, the custodial parent is the one with the highest adjusted gross income. It is also possible for the non-custodial divorced parent of a child to claim them on their taxes if the custodial parent signs and files the proper forms with the IRS. It's important that you come to some understanding of who claims the child on their taxes to avoid a situation in which you both attempt to, and possibly worth working with a CPA to get the situation figured out at least the first time.

This question is better asked of an accountant or a federal tax attorney.

Contact an accountant-but I believe that Federal Guidelines indicate that the parent receiving support is entitled to the deduction. That can be overruled based upon agreement or intervention by the court.

As you can already tell most lawyers do not give tax advice. This is a question better suited for your tax preparer or tax attorney or accountant