The applicant must give notice of his intention to seek an appointment informally to any person having equal right to appointment not waived in writing and filed with the court. The notice shall state that, if no objection or nomination of another or no competing application or petition for appointment is filed with the court within thirty days from mailing of the application and notice, the applicant may be appointed informally as the personal representative. If an objection, nomination, application, or petition is filed within the thirty day period, the court shall decline the initial application pursuant to § 62-3-309. The court may require a formal proceeding to appoint someone of equal or lesser priority.