Quick answer: start at the Register of Wills for a Small Estate Affidavit or Short Certificate, then bring it to the DMV — not the other way around.
The Register of Wills comes first, by design
One document covers cars, trailers, and boats
The Division of Motor Vehicles and the Department of Natural Resources and Environmental Control (DNREC) both require an original Small Estate Affidavit or Short Certificate to transfer title to a deceased person's motor vehicle, trailer, or boat — the same document, regardless of which of the three it is.
A specific order of next of kin without a will
Small estate affidavits are issued to the named executor in a valid, self-proven will. Without a valid will, the affidavit goes to the closest next of kin in order: spouse, children (at least 18 years), parents, siblings, grandparents, and so on.
The same 30-day wait applies
The affidavit process isn't available until 30 days have passed from the date of death — the same waiting period that applies to Delaware's small estate procedure generally.
A local probate attorney can review your estate — many offer a free consultation.
Each of Delaware's three county Registers of Wills — New Castle, Kent, and Sussex — issues this same affidavit before the DMV or DNREC will act on it.