I found an excellent book on tugs and towing designed for professional mariners that covers everything you wanted to know and were afraid to ask about tug towing. Its called "Tugs, Towboats and Towing" by Edward M.Brady, Corenell Maritime Press of Centreville, Maryland.. I got my copy through ebay.
Its been my understanding that, on European still tugs, where the tow hook is midships, that the hawser runs free over the stern and a bridle rope (gog rope?) comes through the aft eyes on the deck then up to the hawser. The bridle rope can be drawn in or out to control the swing of the hawser and its relative postion to the tug during a tow. In that case the hawser will pass over the clearance bows over the deck, rather than under them..
oldiron