Who succeeded William I as ruler of Normandy and king of England?

In accordance with feudal custom, William I bequeathed his lands to his sons, separating the inheritance of the Duchy of Normandy from the Kingdom of England.1

• Duchy of Normandy: William I was succeeded as duke by his eldest son, Robert II Curthose.1
• Kingdom of England: William I was succeeded as king by his third son (and second surviving son), William II Rufus.12

While Robert II initially held Normandy, William II later became the de facto ruler of the duchy in 1096 after Robert mortgaged his lands to him to fund a crusade. Following the death of William II in 1100, his younger brother Henry I seized the English throne.13