If the application for the letters specified in R. 4:80-1(a) (except letters testamentary) is made to the Surrogate's Court by the person first entitled thereto, no renunciation or notice shall be required; but if the application is made by any other person, the applicant shall file:
(a) The renunciation, acknowledged before an officer qualified to take acknowledgments of deeds, of all competent adult persons whose right to the letters is prior or equal to that of the applicant, containing a request that the letters issue according to the application; or
(b) proof that at least 10 days' notice of the application has been given to all such persons residing in this State who have not renounced, and that at least 60 days' notice, or such notice (not less than 10 days in length) as the Surrogate's Court by order may have directed, has been given to all of them who reside outside this State. If in an application for letters of administration with the will annexed, it appears that the decedent left a will naming an executor who has not renounced, proof shall be submitted showing that like notice has been given to the executor. In any case the Surrogate's Court may require the applicant to give notice to interested persons other than those entitled to letters. Such notice may be served either as prescribed by R. 4:4-4 or by registered or certified mail return receipt requested to the person's last known address. If the name or address of any such person entitled to notice is not known, then an affidavit of inquiry as to such name or address, made as prescribed by R. 4:4-5(c) shall be filed in lieu of proof of notice.
(c) In addition to the proofs required in paragraphs (a) and (b) of this rule, if the application for letters of administration shows that there are no known next of kin or knowledge thereof, the applicant shall file proof that at least 20 days' notice of the application has been given to the Attorney General of this State.
(d) All renunciations shall be recorded by the Surrogate's Court.