Del. Code tit. 12 § 1567
The power of a domiciliary foreign personal representative under § 1562 or § 1565 of this title shall be exercised only if there is no administration or application therefor pending in this State. An application or petition for local administration of the estate terminates the power of the foreign personal representative to act under § 1566 of this title, but the Court of Chancery may allow the foreign personal representative to exercise limited powers to preserve the estate. No person who, before receiving actual notice of a pending local administration, has changed position in reliance upon the powers of a foreign personal representative shall be prejudiced by reason of the application or petition for, or grant of, local administration. The local personal representative is subject to all duties and obligations which have accrued by virtue of the exercise of the powers by the foreign personal representative and may be substituted for the foreign personal representative in any action or proceeding in this State.
12 Del. C. § 1567