The public administrator shall apply for and may, with the approval of the clerk of superior court, obtain letters on the estates of decedents when:
(1) It is brought to the public administrator's attention that a period of six months has elapsed from the death of any decedent who has died owning property, and no letters testamentary, or letters of administration or collection, have been applied for or issued to any person; or
(2) Any person without known heirs shall die intestate owning property; or
(3) Any person entitled to apply for letters of administration shall, in writing, request the clerk to issue letters to the public administrator as provided in G.S. 28A-5-2(c).