Depends on to what era you are referring.
Prior to the practice of power running through, engines were generally assigned to divisions.
In later years, the J's, L's, and S's ran HM to Buffalo, Collinwood, or Chicago depending on the train and whether or not it entered CUT. Collinwood to Linndale was electrified, so there were duplicate facilities in Cleveland.
Power on the Ohio State Limited ran through to destination as #15 bypassed CUT.
All 3 St. Louis trains ran via CUT, so they changed.
After the CUT electrification was abandoned, power generally ran through unless cycled out for maintenance.
Same situation at Detroit with the Detroit River Tunnel electrification and the 3 Buffalo / Chicago trains.
Hope this helps.