When I click the middle mouse button (the wheel button) on my empty desktop one of the following happens:

1. A small yellow note appears.
2. A menu with two items ("Web Browser" and "Note") appears. They open what they say.
3. Nothing happens at all.

All of these seem to appear somewhat randomly to me. Anyone could explain the conditions required for each behaviour?

Middle mouse button have paste function. If you have something on clipboard, it appears like in 2nd one. Otherwise 1 or 3.

Starting with KDE 4.4, you can configure the desktop mouse actions via right-click on desktop -> Desktop Activity Settings -> Mouse Actions.
Previous versions mapped the middle mouse button to the paste action which will create a note on the desktop with the current clipboard contents. The menu probably appears if what is in the clipboard is recognized as a web url. If the desktop is locked then nothing will happen (can't create a note on a locked desktop).

All right, pasting notes makes sense. Quite a nice feature.

airdrik wrote:The menu probably appears if what is in the clipboard is recognized as a web url.

Actually, I've just tried copying a URL and I got a note instead of the menu. Are these features documented anywhere so I could check?

Not sure if they are documented but if you enter 'touch' in Search you should get one if not two touchpad configuration options. kcm-touchpad offers a wide variety of options.