(a) Grants of letters of administration and probate
Grant of administration to Administrator General in certain cases
13. If, in the course of proceedings to obtain letters of administration under the provisions of section 9, section 10, or section 11, no person appears and establishes his claim to probate of a will, or to a grant of letters of administration as next-of-kin of the deceased, within such period as to the Court seems reasonable,
or if a person who has established his claim to a grant of letters of administration as next-of-kin of the deceased fails to give such security as may be required of him by law,
the Court may grant letters of administration to the Administrator General.