(a) Letters of administration with the will annexed, letters of administration, letters of ancillary administration with the will annexed and letters of ancillary administration shall be granted by a Register of Wills to such person or persons as shall be entitled to such letters under this section upon their giving bond in accordance with this title.
(b) (1) The persons entitled to letters of administration shall be those in the first of the following classes of persons which shall have a member of that class living and not under an incapacity:
(2) If there shall be more than 1 person living in the first qualifying class mentioned in paragraph (b)(1) of this section, letters of administration shall be granted to all of those persons in the class who give the necessary bond, do not renounce or who are not incapacitated.
(3) If all of the persons in the first qualifying class mentioned in paragraph (b)(1) of this section shall fail to give the necessary bond, renounce or are incapacitated, a Register of Wills shall grant letters of administration to such person or persons as all of them in that class who are not under an incapacity shall have agreed to in writing.
(c) If all of the persons specified in the first class in paragraph (b)(1) of this section which shall have a member of that class living and not under an incapacity shall fail to give the necessary bond, renounce or are incapacitated, and if all of them who are not under an incapacity fail to agree in writing on a person or persons to whom letters of administration shall be granted as provided in paragraph (b)(3) of this section, then any or all of those who fail to agree may petition the Court of Chancery for the grant of letters of administration to their nominee or nominees, and the Court shall grant letters of administration to such person or persons as it, in its discretion, shall determine.
(d) If there shall be no person living in any of the classes specified in paragraph (b)(1) of this section who is not under an incapacity, or if no petition for administration is filed within 60 days from the date of death, then the Register of Wills shall grant letters of administration to such person or persons as the Register, in the Register's discretion, shall determine.
(e) Any interested person may petition the Register of Wills of a proper county for the appointment of an administrator.