“Leaning out” is the layperson term that comes to mind, but I’m supposing a technical and standardized term exists: indirect towing.
Let’s watch the evolution with Capt. Brian and OOCL Berlin. At 12:01, the line is slack.
12:02. As the tow approaches Bergen Point, line is tightened and
by 12:04, the line lengthened, and the tug appears to be headed in a diametrically opposite direction, in spite of OOCL Berlin‘s much larger mass.
Capt. Brian is now using the hull as a brake.
Three other tugs are working alongside the ship.
A different day, Capt. Brian is working on Gjertrud Maersk using the same technique.
All photos and conjecture on the language by Will Van Dorp. Here’s one of my sources. I hope someone corrects or confirms my understanding here.
tugster: a waterblog 
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December 28, 2018 at 1:16 pm
Jim M
Will-
My experience is in under 50’ boats and in kayaks on both salt water and on rivers.
When I see your pictures of the large angled “leaning out”, I can’t help getting a bit of pucker factor concerning the tug being tripped or capsized by the ship.
Although our tonnages are quite different, the physics and hydrology are quite similar to a kayak getting sideways in fast current on a small river.
Reading your included link on towing, I see that my concerns are very possible. Quoted from the link:
“Significant heeling can occur during indirect towing. The tug operator must be extremely careful not to trip the tug as it heels over and nears deck edge immersion. Tractors with flat plate skegs must be extremely careful in conducting this maneuver at speeds over eight knots as the skeg can dig in too hard and potentially cause the tug to trip before the operator can recover from the maneuver.“
Thanks for posting this, the maneuvering and boat handling is fascinating!
All the best for a happy and healthy new year!!
Jim
December 28, 2018 at 6:15 pm
Anonymous
Will,
Phantastic photos. Thank you. Grew up hanging out on the docks on the North River (Hell’s Kitchen) – the funnels of the Queen Mary and Queen Elizabeth parked at Pier 92 was the scene out my bedroom window.
My best for you and your family in the New Year.
UncleSlick