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If the property was properly transferred into the trust (usually to the trustee). Then the process should be fairly simple. For example, if the property is in Oklahoma there would be an affidavit of successor trustee and a trustee’s mineral deed. Currently Oklahoma does not require any court oversight. Other states may have different requirements.
One common problem is people who forget to deed their minerals into the trust. If this occurs then that state’s probate or probate substitute procedures must be followed.