In 1144, Geoffrey, count of Anjou (1113-1151), became Duke of Normandy by conquest. His son, Henry, controlled Aquitaine and Poitiers by virtue of his marriage to Eleanor of Aquitaine (1152), and became Henry II of England on the death of Stephen in 1154. Henry required Malcolm IV (then aged 12) to swear homage to him in 1157; in Wales, he claimed - but could not establish effectively - overlordship; and although he invaded Ireland in 1171-2 and received the homage of the native Irish kings, his authority was tenuous. He declared his nine-year old son John Lord of Ireland. John was not effective in subjugating Ireland, and managed to lose most of the territories held in France to the French king, Philip II.
According to wikipedia (2017), "At its largest extent, the Angevin Empire consisted of the Kingdom of England, the Lordship of Ireland, the duchies of Normandy, Gascony and Aquitaine as well as of the counties of Anjou, Poitou, Maine, Touraine, Saintonge, La Marche, Périgord, Limousin, Nantes and Quercy. While the duchies and counties were held with various levels of vassalage to the King of France, the Plantagenets held various levels of control over the Duchies of Brittany and Cornwall, the Welsh princedoms, the county of Toulouse, and the Kingdom of Scotland, although those regions were not formal parts of the empire. Auvergne was also in the empire for part of the reigns of Henry II and Richard, in their capacity as dukes of Aquitaine. Henry II and Richard I pushed further claims over the County of Berry but these were not completely fulfilled and the county was lost completely by the time of the accession of John in 1199" (https://en.wikipedia.org/w/index.php?title=Angevin_Empire&oldid=767203721).
For more, see Gillingham (2001).