How come commonwealth countries have prime ministers, yet are independent from their former empires?
Ok. First up, there’s only one empire which became the basis of a Commonwealth, and that’s the British one. Now the countries in the British Empire, at various times, decided that they wanted independence (although some took longer to decide to completely sever their ties, New Zealand is an example.) The prime minister is the head of a democracy elected by the people of that country, with no involvement from Britain. All of those Commonwealth countries agreed they wanted independence, but also wanted to stick together in a kind of brotherhood (although countries are always referred to as her… *ponders*) The only representative of the Queen (head of the Commonwealth) in any country is the Governer-General, whose role in this day and age is mainly just for the title and not for anything too important in terms of the affairs of the country.