OneNote 2016 Desktop (O.N.) version (and perhaps other versions - I have it installed on Windows 10x64) allows you to dock a window. Pressing "Dock to Desktop" in the View menu does the following. The O.N. section window is moved to either the left or right side of the screen, giving it a certain pixel width (this is presumably based on the last place you placed or resized the dock to).
In order of importance, the docked window also has these features:
In other (non-docked) windows, if you press their respective maximize button, their respective window will cover only the section of the screen outside of the dock.
It is always on top
Its width can be adjusted with the mouse
It can be dragged to change screen sides or moved to another monitor
I am seeking software that can do this with any type of window (web browsers etc.) and not just OneNote (however it would seem that you choose one window per monitor side to dock, so if you have 2 monitors, max of 4 docked windows, that is left and right of both monitors).
There are plenty of programs that allow you to arrange your windows in certain ways (DisplayFusion, AquaSnap, WinSplit) and there are Windows keys to snap them , but I am specifically seeking this "Dock Window" function that includes the above especially with feature 1.