The rules that govern when and how appellate courts can decide cases is called jurisdiction. There is some discussion of this in the Appeal and Review Bar book but they do not directly address what this does to the trial court's jurisdiction
When a notice of appeal is filed with the trial court the Court of Appeals gains exclusive jurisdiction, excluding certain specific matters, in civil (ORS 19.270) and criminal (ORS 138.083) cases. This is when the Court of Appeals gains control of a case and deliberates on the matters raised in the appeal.
When the Court of Appeals issues a judgment in an appeal that decision is communicated to the trial court pursuant to ORAP 14.05 and the trial court then regains jurisdiction over the case (ORS 19.270 and ORS 138.227). As Martineau puts it in Modern Appellate Practice section 17.2:
An appellate court decision on any aspect of the case becomes the law of the case and is controlling on the trial court and on any further appeals in the same case.
Thus at the end of an appeal, absent a petition to the Supreme Court or the federal courts, the trial court regains control or jurisdiction over a case and proceeds according to the judgment.
