In Ohio, if a person dies without a valid will and the deceased had probate property (see http://www.perlalaw.com/blog/what-is-probate-property-and-why-do-i-need-it-for-my-will-to-operate/), the Probate Court in the county where the person died will need to appoint an Administrator.
When determining who should be appointed Administrator of an estate, the Court will go through candidates in order of priority. First, the surviving spouse, if a resident of the state of Ohio. Second, the next of kin of the deceased, if a resident of the state of Ohio. If there is no spouse or next of kin able to serve, or if they neglect to apply with the Probate Court for the position within a reasonable time, they lose their priority, and the Court will appoint a suitable person who is an Ohio state resident.
In order to be appointed administrator, an application must be filed with the Probate Court which contains the name and address of the surviving spouse and next of kin, if known by the applicant, as well as a general statement as to what property is in the estate and its probable value as well as a statement of the debts owed by the deceased to the applicant. If there are others who have priority to administer the estate ahead of the applicant, the individuals with priority will have to sign waivers or will be served by Probate Court to determine whether they would like the position. If there there are multiple next of kin who wish to serve as Administrator, a Hearing may be necessary to determine which candidate will be appointed.