Any persons willing to become parties to an amicable action may enter into an agreement in writing for that purpose, either personally or by their agents or attorneys. On filing such agreement with the Prothonotary, the Prothonotary shall docket the action in the Superior Court, and from the time of such entry the action shall be deemed to be depending in the same manner as if the defendant had appeared to a summons issued against him or her by the plaintiff.
10 Del. C. § 3109