Final answer:
The majority of cases in the federal courts of appeals come from U.S. District Courts, with some originating from specialized federal trial courts. The appellate system includes thirteen U.S. courts of appeals, serving as the intermediate level between the district courts and the U.S. Supreme Court.
Step-by-step explanation:
Most of the cases that reach the federal courts of appeals originate from the lower tier of the federal judicial system, which is the U.S. District Courts. These district courts act as trial courts where cases are first heard. If parties involved in the litigation are not satisfied with a decision at the district court level, they have the right to appeal to the circuit courts, which are also known as the U.S. courts of appeals. Furthermore, there are specialized federal trial courts, such as the Court of International Trade and the Court of Federal Claims, whose decisions may also be appealed to the circuit courts and, on rare occasions, to the Supreme Court.
Within the federal appellate system, there are thirteen U.S. courts of appeals, which are divided into twelve regional circuits, along with the Federal Circuit, which has nationwide jurisdiction. These appellate courts are considered intermediate appellate courts because their decisions can be further appealed to the U.S. Supreme Court.