Subject-matter jurisdiction examples: State courts, Federal courts, U.S. Supreme Court.

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1.  State trial courts have subject-matter jurisdiction over all cases except those which must be heard exclusively in other courts.  Paul files a tort case against Dennis in a state trial court.  There is no law which gives any court exclusive jurisdiction to hear this type of case.  Therefore, the state trial court has subject-matter jurisdiction over this case.

2.  Federal district courts are courts of limited jurisdiction.  They only have subject-matter jurisdiction if a claim arises under federal law, or if no plaintiff shares a state of citizenship with any defendant and the amount in controversy exceeds $75,000 (see diversity jurisdiction).  Richard thinks that Vincent has violated federal racketeering law, and wants to file a civil suit.  Richard and Vincent are both citizens of New York, but the case can still be tried in federal district court because the claim arises under federal law.  Alternatively, the case may be tried in state court because no law gives federal courts exclusive jurisdiction over this type of claim.  

3.  The State of Arizona plans to sue the State of California for excessive air pollution amounting to a public nuisance.  Under 28 U.S.C. § 1251, the U.S. Supreme Court has exclusive jurisdiction over "all controversies between two or more States."  This means that only the U.S. Supreme Court has subject-matter jurisdiction over this type of case.  Arizona can only sue California in the U.S. Supreme Court.  The state courts have no subject-matter jurisdiction over this type of case.