The U.S. Supreme Court case Arkansas v. Tennessee in 1969 involved a dispute over the boundary line between the two states due to changes in the course of the Mississippi River, which serves as their border. The controversy arose when an avulsion (a rapid change in river flow) occurred around 1821, causing confusion about whether it changed state boundaries or not. The court ruled that an avulsion does not alter borders and therefore upheld Tennessee's claim to sovereignty over certain disputed lands on its side of the river based on historical precedent set by previous cases such as State of Indiana v. Kentucky (1890). This decision was grounded on principles established under common law tradition and international law regarding riparian boundaries - that is, those formed by rivers or other bodies of water.

In the dissenting opinion for the case of Arkansas v. Tennessee, Justice Black disagreed with the majority's decision to award a disputed tract of land to Tennessee based on avulsion theory. He argued that there was insufficient evidence presented in court to prove that an avulsive event had occurred which would have suddenly and noticeably changed the course of Mississippi River, thereby shifting state boundaries. Instead, he believed that gradual erosion and deposition processes known as accretion were responsible for altering river’s path over time. According to him, these changes should not affect established state lines under existing legal principles governing boundary disputes between states. Therefore, he contended that Arkansas should retain ownership over this contested area because it fell within its original territorial limits before any alleged geographical changes took place.