The probate packet
When someone died owning property, the county probate court opened a case file. That packet typically includes the will (if one was written), the petition for probate naming the heirs, letters testamentary or letters of administration, an inventory of the estate, accounts of sale, the distribution, and final discharge. Each document is dated and signed — the petition alone often names every surviving child, their spouses, and their places of residence.
If the decedent died intestate, administration files are if anything more genealogically useful than wills because the court must formally identify every legal heir.
Latin and legal shorthand
Probate is the densest source of Latin after church records. Common terms: relict (surviving spouse), et al. (and others, usually 'and other heirs'), in ventre sa mère (a child unborn at the father's death), filius/filia (son/daughter in older records), and per stirpes vs. per capita (distribution rules that change which grandchildren inherit).
Abbreviations: exr. (executor), admr. (administrator), adm. c.t.a. (administrator with the will annexed), d.b.n. (de bonis non, 'of the goods not yet administered' when an executor is replaced mid-case).
Where probate lives
County clerk, probate court, or surrogate's court — the title varies by state. Many pre-1900 files have been microfilmed and are free at FamilySearch. For post-1900 cases, the county-level court is the authoritative source; small counties are often willing to mail copies for a small fee. State archives hold older files that rural counties transferred out for climate control.