In legal terminology, what you're describing is a civil lawsuit, where two parties, in this case, Aquaman and King Triton, are in a legal dispute over a claim of control or jurisdiction over the ocean.
In this scenario, each party (also known as the litigants) would present their case before the court, likely employing the services of legal counsel (attorneys or barristers) to argue their positions. Evidence would be presented, and through a process of legal argument and decision-making, the court would make a ruling, or judgement, on the matter.
Keep in mind, however, that the unique nature of this case (involving fictional characters and a jurisdiction, the ocean, that is not typically subject to individual control) could present unique challenges in the legal system. The court would need to determine if it has the authority or jurisdiction to make a ruling in this case, and what laws or precedents apply.
It's also interesting to note that in most legal systems, natural resources such as the ocean are considered common heritage or public goods, and cannot be owned or controlled by individuals or entities. Therefore, the claim by Aquaman and King Triton to have "say over who runs the ocean" might not be legally valid or enforceable.