Iowa Code § 633.639

The title to all property of the protected person is in the protected person and not the conservator subject, however, to the possession of the conservator and to the control of the court for the purposes of administration, sale, or other disposition, under the provisions of the law. Any real property titled at any time in the name of a conservatorship shall be deemed to be titled in the protected person’s name subject to the conservator’s right of possession.