Subject to the rules and regulations of the Board of Human Resources, the county department shall be charged with the administration of all forms of public assistance in the county, including home relief; indoor and outdoor care for those in need; temporary assistance for needy families; old-age assistance; aid to the blind and otherwise disabled; the care and treatment of dependent, neglected, delinquent, and disabled children; and such other welfare activities as shall be delegated to it by the Department of Human Resources or by the county commissioners. The county department shall also investigate and pass upon all applications for admission to and discharge from county institutions which provide care and treatment for indigents. If so appointed by a court of competent jurisdiction, the Department of Human Resources or the county or district department of family and children services shall perform under the supervision of such court the function of probation officer or agent of the court in any welfare or penal matters which may be before it.