Does the court take a percentage of the inheritance when it is divided and checks are issued, or is the full amount distributed to the heirs?

If you are asking about the permissibility of the court taking a fee in exchange for dividing an inheritance, the basic principle is that a judge who receives a salary from the public treasury (Bayt al-Mal) is not permitted to take a fee for his judgments. This is because the judiciary is compensated from the public treasury, and it is not permissible to take a fee for it. Anyone who is sufficiently provided for from the public treasury of the Muslims is not allowed to take a fee from the litigants.