§1. The petitioner can renounce the trial at any stage or grade of the trial; likewise both the petitioner and the respondent can renounce either all or only some of the acts of the process.
§2. To renounce a trial, guardians and administrators of juridic persons need the counsel or consent of those whose involvement is required to place acts which exceed the limits of ordinary administration.
§3. To be valid, a renunciation must be written and signed by the party or by a procurator of the party who has a special mandate to do so; it must be communicated to the other party, accepted or at least not challenged by that party, and accepted by the judge.
Source: Code of Canon Law (Vatican.va)