(a) The Register of Wills shall have power to take acknowledgements, administer oaths, issue notices, certify and authenticate copies of instruments, documents and records of the Court and perform the usual functions of the Register's office.
(b) If a matter is one with respect to which no notice is required by statute or rule of court to be given to any person then, except as otherwise provided in this title or by rule of court, the Register of Wills may hear and determine it and make all orders, adjudgments and decrees in connection therewith which the Court of Chancery could make, subject to being set aside or modified by the Court at any time within 30 days thereafter; and if not so set aside or modified such orders, adjudgments and decrees shall have the same effect as if made by the Court.
(c) All actions commenced in the Court of Chancery shall be filed with the Register in Chancery, who shall have custody of the records thereof, as provided by the Rules of the Court of Chancery, notwithstanding that such action may be brought upon a cause of action previously within the cognizance of the Register of Wills.
(d) Without limiting the generality of the foregoing, the Register of Wills shall have such further powers and duties as may be specifically conferred upon the Register by statute or by rule of the Court of Chancery.