The original question was about maximum effective power and efficiency.
It’s exactly as Kennebec Captain stated: one slow speed (about 100 rpm) direct reversible engine turning one large propeller.
For a lot of reasons: safety and environmental protection being foremost, virtually all tugs are now twin screw with one engine each shaft.
I do not think that the USCG allows any single screw tug to tow an oil barge.
The few single screw tugs that I still see in service are doing harbor work, or towing logs, wood chips, salt, cement, gravel, riprap, and other low value, low environmental risk cargoes. I don’t think that most customers will accept a single screw tug.
What(and when) was the last U.S. single screw tug built?
Triple and quad screw tugs are built for services where shallow draft is critical. Four screws in tunnels keep the draft shallow and provide the most push for a driven draft at the expense of fuel efficiency and maneuverability (in tunnels).
Twin screw provides maneuverability and redundancy at an acceptable loss of fuel efficiency for most applications.
Diesel electric is the most effective approach for DP applications. Obviously, it would make sense to have several gen sets and only run as many as needed to produce the necessary power for the actual load conditions.
So far, controllable pitch has not caught on for tugs in the U.S. due to its high initial cost.
With the exception of Western Towboat (and Hyak), z-drive has not caught on for linehaul tugs. Z-Drive is reserved mostly for ship escort and ship docking.
Actually, I think Western Towboat is blazing a smart and innovative trail into Z-drives for linehaul tug boats that will be increasingly imitated. They probably have less initial and everyday cost efficiency, but that is offset by increased maneuverability and capability.