N.J. Stat. § 2A:23A-15
When a party dies after making a written agreement to submit a controversy to alternative resolution, the proceedings may be initiated or continued upon the application of, or upon notice to, the party's executor or administrator or, when it relates to real property, the party's distributee or devisee who has succeeded to the party's interest in the real property. When a custodian of the property or a guardian of the person of a party to an agreement is appointed, the proceedings may be continued upon the application of, or notice to, the custodian or guardian. Upon the death or incompetency of a party, the court may extend the time within which an application to confirm, vacate or modify the award or to stay alternative resolution must be made. Where a party has died since an award was delivered, the proceedings thereupon are the same as when a party dies after a verdict.
N.J.S. § 2A:23A-15