CakePHP AJAX country region select box (combo box)

How to setup dynamic AJAX country region select boxes (aka combo boxes) using the CakePHP framework and the AJAX Helper.
This is a classic problem : you have a country select box in a sign up form and you want to update a region select box (or states, or other administrative country division)  when the user chooses a country. Without refreshing the whole page and using AJAX off course.
CakePHP’s AJAX helper allows to quickly implement this.
If you want a quick and easy way to implement a select box update using AJAX and CakePHP download the example files bellow :
Online demo here : CakePHP AJAX country region select box
Example files :
CakePHP AJAX combo box example files