The US Supreme Court is an appellate court, and therefore does not try cases or determine facts of the case, rather it interprets facts of law, and may grant new trials. There is no right to an...
There is only one United States Supreme Court, but there are also State Supreme Courts. So, to answer your question: none. The U.S. Supreme Court is it's own court.
In the UK, it would be the High Court of Justice (Chancery Division). In the US, it varies by State but would usually be an intermediate court in the State's legal system.