Del. Code tit. 12, § 3531

Whenever, by any will, deed or other instrument, a trustee is named and before the acceptance of the trust the person named as such trustee renounces and declines to perform the duties imposed thereby, the trustee may make and file in the office of the Register in Chancery of the county where such will, deed or instrument may be probated or recorded a written renunciation setting forth in general terms the instrument of appointment and that trustee has not accepted the trust or exercised any powers or performed any duties thereunder and trustee declines to act under such appointment. The Register in Chancery shall record and index such renunciation in the Chancery docket.