The register or clerk shall, within 30 days from the entry of a judgment under this division, file the same or a certified transcript thereof for record in the probate court of the county in which the land lies and tax the expense thereof in the costs of the case. The probate judge shall record the judgment in the same book and manner in which deeds are recorded and index the names of defendants or parties against whom the relief is granted in the direct index and the names of the plaintiffs or parties quieted in possession of the land in the reverse index.