Quick answer: Delaware assigns jurisdiction over decedents' estates to the Court of Chancery — the same equity court best known nationally for corporate law disputes. Day-to-day filing runs through the county Register of Wills, which acts as that court's Clerk. See how this affects your own estimate in the Delaware probate timeline calculator.
An equity court's estate jurisdiction
Register of Wills: the day-to-day face of the court
For a routine, uncontested estate, families interact almost entirely with the Register of Wills in whichever of Delaware's three counties — New Castle, Kent, or Sussex — the decedent lived. Each Register acts as a Clerk of the Court of Chancery, handling filings, fee collection, and the administrative side of the process. A Chancery judge typically becomes directly involved only when a matter is contested or otherwise requires formal court action.
Where the expertise actually shows up
For a simple estate, this structure changes little day to day. Where it matters is in a genuinely contested matter — a will contest, a dispute over an executor's conduct, or a fight among beneficiaries. Because Court of Chancery judges specialize in fiduciary and equity law rather than rotating through a general docket, a contested Delaware estate benefits from unusually deep judicial expertise on exactly the kinds of questions such disputes raise.
A local probate attorney can review your estate — many offer a free consultation.