 It shares jurisdiction with the county courts, and in some case justice of the peace courts, for civil cases (its lowest limit for hearing a case is a mere $200 in controversy, while JP courts can hear cases up to $10,000).Family law jurisdiction varies depending on the existence of a county court-at-law; in some counties, the district courts share jurisdiction over divorces, child custody and support matters, adoptions and child welfare cases with county courts at law.Probate jurisdiction varies, depending on the existence of a statutory probate court in the county.