As an adult, Harry now could claim the Lord Potter ring, by blood; but Harry also was Lord Malfoy and Lord Nott, by Right of Conquest. It turned out that when the previous Lord Malfoy and Lord Nott each had attacked Harry and had tried to kill him, but Harry instead had killed them, Magic had awarded Harry their titles, their coins, their properties, and their Head of House statuses. The Heir Nott title no longer belonged to Theodore Nott, and Heir Malfoy no longer was Draco Malfoy’s title; those heirships would go to whomever Harry chose, and he was not bound by previous family law.