A trial is only held if a jury is demanded by the defendant. The plaintiff/sovereign does not need a jury because he is the tribunal. It is the defendant who needs jury protection from the plaintiff/sovereign/tribunal.
Also, if all defendants demur, then the court has the option of either conducting a trial, or producing a judgment.
There is no appeal from the decision of a court of record, except by the rules of the common law (i.e. a new trial with a jury).