(a) Every decree of distribution made by the Court of Chancery in a proceeding initiated under this subchapter shall be a final decree, but the personal representative of the decedent or any person claiming to have an interest in the estate thereby decreed to be distributed shall have the right, at any time within 30 days after the making and entry of such decree, to take an appeal therefrom to the Supreme Court. After the expiration of the period of 30 days such decree of distribution, with respect to all matters contained therein, if no appeal has been taken therefrom, shall become and be conclusive and binding upon the executor or administrator of the estate of the decedent and upon every person claiming to have an interest in the estate thereby distributed.
(b) If an appeal is taken from any such decree, the decree or judgment made and entered by the Supreme Court on such appeal shall likewise be conclusive and binding upon the executor or administrator and every person claiming as aforesaid, from the date of the making and entry of the decree or judgment by the Supreme Court.
(c) Any appeal taken to the Supreme Court shall be heard by that Court upon the record of the proceeding in the Court of Chancery and the procedure on such appeal shall be in accordance with the rules of the Supreme Court.