Taking this off topic...but I can tell you that twice in my life I was moved on UA. (happen to BOTH be out of the same station) Once was a few weeks ago.

I was called to the podium and it was REQUESTED if I would move because the g/a wanted to get a mom/son together. This was a E+ window for E+aisle. I do NOT like aisles. I requested another E+ window, and he stated he didnt have one, but would get the next pax. I took the seat...telling him it wasnt a big deal.

Well..big deal it was!!! As I boarded, he handed me a F bp for my connecting flight, and smiled and thanked me again for changing seats.

So...just a VERY VERY small sample, but this is how UA does it.