The Duchy of Cornwall is a duchy in England. The eldest son of the reigning British monarch holds the title Duke of Cornwall (female: Duchess of Cornwall). The current duke is Prince William.
The Duchy has no control over Cornwall itself but is just largely located there. The Duchy of Cornwall is a collection of land belonging to the Duke.
When the monarch has no male children, the monarch holds the title.
The Duchy belongs to the monarchy and does not pay corporation tax.