Explain how and why colonies of the world’s most powerful empire developed unique, independent system of governing

The colonies under the Great Britain Empire were situated on the other side of Atlantic Ocean, this performed a role of a divide between the Rulers (The Britain) and the subject (Colonies).
This fact hindered direct and frequent involvement of Britain to the colonies. The situation allowed the subject and rulers there to expand in various ways as well as establish a democratic regime gradually resulting in a unique, independent system of governing.