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George III's successor was his eldest son who was Regent for a number of years before his father died (when he was still the Prince of Wales). He succeeded to the throne as George IV and had only one legitimate child who would have been queen had she not died at the age of twenty one I believe on the birth of her first child. He did have several children who strictly speaking would have more claim to the throne than our present lot had his first marriage to a commoner been recognised.