In any case in which a defendant waives his right to trial by jury and elects to be tried by the court under section 2945.05 of the Revised Code, any judge of the court in which the cause is pending shall proceed to hear, try, and determine the cause in accordance with the rules and in like manner as if the cause were being tried before a jury. If the accused is charged with an offense punishable with death, he shall be tried by a court to be composed of three judges, consisting of the judge presiding at the time in the trial of criminal cases and two other judges to be designated by the presiding judge or chief justice of that court, and in case there is neither a presiding judge nor a chief justice, by the chief justice of the supreme court. The judges or a majority of them may decide all questions of fact and law arising upon the trial; however the accused shall not be found guilty or not guilty of any offense unless the judges unanimously find the accused guilty or not guilty. If the accused pleads guilty of aggravated murder, a court composed of three judges shall examine the witnesses, determine whether the accused is guilty of aggravated murder or any other offense, and pronounce sentence accordingly. The court shall follow the procedures contained in sections 2929.03 and 2929.04 of the Revised Code in all cases in which the accused is charged with an offense punishable by death. If in the composition of the court it is necessary that a judge from another county be assigned by the chief justice, the judge from another county shall be compensated for his services as provided by section 141.07 of the Revised Code.