Which of the following is recognized as the official residence of the Pope?

The Vatican Palace is recognized as the official residence of the Pope, also known as the Apostolic Palace. This grand structure is located within Vatican City and serves not only as the Pope’s living quarters but also as the administrative headquarters of the Catholic Church. It contains numerous rooms, chapels, and halls, including the famous Sistine Chapel and the Vatican Museums, showcasing the rich history and spiritual significance of the papacy.

Vatican City, while it is the independent city-state and home to the Vatican Palace, is not specific enough to indicate the official residence itself. Rome, as the larger city surrounding Vatican City, does host many significant churches and the broader context of the Catholic Church but is not the Pope's residence. Similarly, Florence, although historically significant in Italian culture and art, has no connection as the residence of the Pope. The Vatican Palace thus stands out as the correct answer due to its unique role and designation within the context of the papacy and the Catholic Church.