Does the trial court have jurisdiction over a cause during the pendency of an appeal?

Does the Court have jurisdiction over a cause in the trial court during the pendency of an appeal? (California, United States of America)

Does the Court of Appeal have jurisdiction to order an order affecting a judgment from the trial court while the appeal is pending? (California, United States of America)

When a cause of action on appeal from a trial court's order sustaining demurrer is not discussed in the brief, is it abandonment of that cause? (California, United States of America)

When a defendant makes a mid-trial motion to revoke his self represented status and have standby counsel appointed for the remainder of the trial, does the trial court have a duty to manage the trial? (California, United States of America)

Does a judge have jurisdiction to hear an appeal from the Superior Court of the Court of Appeal? (California, United States of America)

Can a defendant bring a notice of appeal to the Court of Appeal claiming that he failed to raise his constitutional claims in the trial court? (California, United States of America)

On a motion to be heard by the Court of Appeal at the Superior Court of California for a change of venue, does the Court have any jurisdiction or authority to hear the motion? (California, United States of America)

Does the majority opinion in the Supreme Court of Canada say that a trial court lacks subject matter jurisdiction pending an appeal? (California, United States of America)

When a court of appeal has an appealable judgment or order before it, does the court have jurisdiction to affirm, reverse or modify it? (California, United States of America)

In a motion for a new trial, is the trial court bound by the same principles as the court of appeal? (California, United States of America)