Superior courts are Arizona's trial courts, and there's at least one in each county. Arizona superior courts handle divorces, evictions, small claims, tax, probate and juvenile matters, and also hear appeals from municipal and justice courts. Arizona's municipal courts mainly handle misdemeanor crime and violation of city ordinance cases. Arizona's justice courts (aka Justice of the Peace courts) can also hear these cases along with domestic violence, assault and battery, and general civil cases. The Arizona state court system also includes it's appellate courts and the Arizona Supreme Court.
Arizona court's online system, Public Access to Court Case Information, (http://apps.supremecourt.az.gov/publicaccess/caselookup.aspx) allows users to get information about Arizona state court cases when searching by name, date of birth, or case number. If you're trying to research if someone has ever been sued, or if they have a criminal record in Arizona, you could use this website to find out. However, the database only provides basic information including party names, charges, and any decisions made. If you're seeking public court records in Arizona, you'll need call, visit, or send a written request to the Clerk of Courts office in the county where the case took place.