The Trustee of a Trust must execute the transfer of deeds for any real property owned by the Trust that is sold to a new owner.
Further, if the Trust is revocable, then the Grantor of the Trust can terminate the current Trustee and name a new Trustee (i.e. the person who may sign deeds for real property), if that is the requirement set forth in the Trust or if that is the direction the Grantor decides.
But given these two statements of required action by the Trustee, the mental competency of the Grantor is a separate matter entirely.
If a Grantor is mentally incompetent to handle the decisions related to the Trust going forward, such a designation must be made by a court.
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