Question

Trying to remove an appended div, I’ve tried .empty() and contents().remove();

I’ve commented out the removed code, see: http://jsfiddle.net/2Aw23/2/

Answer 1

Is this what you want?

JS fiddle demo

It will add the div when the button is clicked, but then remove it when anything else is clicked. But note that other code may also specify that clicks on other parts of the page should stop propagation, so if that is the case, clicking those elements also will not remove the div.