Until 1858 there were many different courts in England & Wales which had the right to prove wills and give grants of administration and most of these were church courts. The Prerogative Court of Canterbury (PCC) was the most important of these courts and it's records are held at the Public Record Office (PRO). Wills proved by other courts are usually held in county record offices and other archives. Details can be found in the FFHS booklet "Probate Jurisdictions: where to look for wills"
In theory, if you had personal property, in only one archdeaconry, your will could be proved in the Archdeacon's court. If you had property in more than one Archdeaconry, but all within one diocese, then your will had to be proved in the Bishops court, usually called a "consistory court".
If you had property in more than one diocese then your will had to be proved in the Archbishop's prerogative court either Canterbury or York- if the property was in more than one ecclesiastical province then it would be proved in both- but only that property relating to the ecclesiastical province. So it could be in both Archbishops courts.
There were notational rules, not always observed in practise that property had to be over £5 in value (£10 in London & Lincoln)
If some one died without leaving a will then the courts could make a grant of administration (Often abbreviated Admon) to the next of kin, principal creditor or any other person who could claim a legitimate interest in the personal property.
Taken from PRO Publications
PC Canterbury Wills and Other Probate Records by Miriam Scott