http://www.gilerafuoco.com/index.html?lang=eng
I’ve seen other bikes with a wider wheel in back, and assumed it was for stability when leaning in on tight turns. The cycle in the first link has two wheels with an independent suspension. Two wheels make the front wider than the back.
Now if I were on a tight turn, the wider front wheel would be closer to the inside of the turn, and would this make the back end of the bike more likely to spin out from under the rider?
on edit: I don’t have the experience to comment on the three wheeler. One of my bikes has a sidecar, and I can assure you that anyone who thinks a sidecar rig is stable is on drugs. They are significantly easier to roll than a mail jeep.
A wide rear tire usually* makes the bike somewhat LESS stable. That is not so bad if what you are looking for is quick handling, say a road racing bike. It may also be needed to give acceptable tire life with a high horsepower engine. 1000+ CC sport-bikes are the only machines that have the power to utilize that much rubber.
There is some merit to your turn idea. A motorcycle tire has a round profile, as opposed to the flat profile of a car tire. This reduces the contact patch when going straight, but allows the patch to be maintained when banked in a turn. A wider tire allows a larger profile radius, which allows a wider contact patch in both conditions.
Note that the link you provided shows a chopper, which IME seldom (if ever) lean even as much as 45 degrees. In the case of choppers, the wide tire is mostly for looks…but not entirely. The extreme steering rake angles used on choppers tends to make them excessively stable. That is they really, really just want to go straight. A wide rear tire can mitigate this to a slight degree. Also, choppers often retain only vestigial front brakes, and the long forks reduce the weight on the front wheel. Due to these factors, and intellectual inertia, rear wheel braking tends to dominate with the riders of such machines. This often leads to skidding, and a wide back tire has more tread area to soak up the wear thus caused.
*Motorcycle stability is a very complex subject, involving:
-Both front and rear tire diameters, profiles, widths, and construction (radial vs bias ply).
-Steering angles (rake and trail)
-Suspension geometry, stiffness, rate, and damping.
-Aerodynamic factors (not so much at low speeds)
-Frame stiffness.
-Other stuff I can’t think of at the moment.
-Rider ergonomics.