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There are two parts of Kashmir, one is Azad Jammu and Kashmir also called Pakistan controlled Kashmir and another is Indian controlled Kashmir.
Pakistan controlled Kashmir (Azad Jammu and Kashmir) have their own capital city, parliamentary government and they elect their own prime minister of state.
Is Pakistan controlled Kashmir (Azad Jammu and Kashmir) an independent state?
Doesn't this Wikipedia article answer your question? It says, in particular,
Azad Jammu and Kashmir, abbreviated as AJK and commonly known as simply Azad Kashmir, is a region administered by Pakistan as a nominally self-governing jurisdiction.
(I added the bold face.)
