If the application is made by the minor's only living parent for letters of guardianship of the minor's estate, no renunciation or notice shall be required; but if made by any other person, there shall be filed either:
(a) A renunciation, made in accordance with R. 4:96-2, by (1) all adult persons whose right to the letters is prior or equal to that of the applicant, (2) the person or persons, if any, in loco parentis to the minor and (3) the persons with whom the minor resides. All such renunciations shall contain a request for the issuance of letters according to the application; or
(b) Proof of notice of the application or affidavit of inquiry as prescribed in R. 4:80-3(b). Such notice shall be given to the persons whose renunciations are required by paragraph (a) and such additional persons as the Surrogate may specify.
