Neutral Wire Size

Neutral of a 240V 1-phase service feed can be sized as a smaller wire. The size must handle the current imbalance between the 2 legs.

https://sparkypedia.electricianu.com/are-we-allowed-to-reduce-the-size-of-neutral-conductors/#:~:text=Because%20the%20neutral%20conductor%20functions,neutral%20conductor%20for%20a%20feeder.

Is this the correct understanding:

1. Center tapped transformer has opposite phases on each side
2. Current cancels itselff out when each side is loaded equally
3. If each side is not loaded equally, then the center wire transfers only the unbalanced current - the balanced part of current cancels itself out.

Note that 120/240V comes from a single phase winding. To get 120, armature of generator is tapped at the center. A 3 phase source has 3 armatures. This is just how the geometry works out.

Do power lines carry 1 phase or 3 phase?