Which IMEs (input method editors) are actually most used in each of PRC, ROC, and Hong Kong?
Many people in Hong Kong use Quick aka 速成 or Simplified Cangjie.
There is a wiki link for this input method:Simplified Cangjie

There is a build-in Quick IME in Windows and Mac. Most of the Quick users use it.

Quick users type Chinese using Quick on smartphone too, as the build-in IME of smartphone that selling in Hong Kong usually support Quick. 

However, some people prefer to type using 5-stroke input method(5筆畫輸入法) on phone. There is a wiki link for this input method:Wubihua method. This is a very simple input method. It is based on the stroke order of a Chinese character so as long as you write Chinese, you will know how to type.