What is the definition of supplemental jurisdiction?

The definition of supplemental jurisdiction is accurately captured by the idea that it refers to a court's authority to hear additional claims that are related to existing claims within a case. This legal principle allows federal courts to exercise jurisdiction over claims that are not independently within their original jurisdiction, provided they are tied to a claim that is already before the court through a common nucleus of operative fact.

This mechanism helps to ensure judicial efficiency by allowing related claims to be litigated together, reducing the need for multiple lawsuits and preventing piecemeal litigation. It signifies that as long as the additional claims share a significant relationship with the primary claim, the court has the authority to hear them even if they would not qualify for jurisdiction on their own.

The other options do not accurately represent supplemental jurisdiction. Dismissal power, unrelated claims, and claim amendment all pertain to different aspects of legal procedure but do not encapsulate the essence of supplemental jurisdiction.