I've sorted it. When you hold on an application in the Dock, it gives you the options of assigning the application in All Desktops, This Desktop, or None. I didn't, and still don't, understand what 'assigning' means. I thought that if I assigned an application to None, then its files wouldn't open in any desktop. Actually, its file will open in any desktop, and I can move it to any other Desktop and it'll stay there. Assigning Stickies, Notes, or Calculator to All Desktops puts all their open files in every Desktop, which is sometimes useful to me. This Desktop means you can do the same as None, but when you close a file and reopen it, it pops up in the original Desktop. I haven't figured out why you would want this to happen, so I'll stick with the other two as convenient.
I wish that the gods of Computing would describe things operationally, because context-free abstract generalisations such as 'assigning' are uninterpretable. Operational definitions comprise specific instructions: do this, then this, and these things in this order, then this will happen. Telling people they can easily 'purge their overload', or just 'add your favourite functionality' isn't helpful unless you tell them exactly how to do it, and why they might want to.
Thanks for your help and patience with my meandering incomprehension.
Bob