He was the son of Ugo degli Alberti of the Counts of Capraia and Bina, the first wife of Peter I of Arborea, whom he divorced in 1191 and who subsequently remarried (1193).
When Peter II of Arborea died in 1241, William immediately assumed the regency with the alliance of the Gherardeschi, counts of Donoratico, and the Visconti.
After fourteen months of war, the deposed judge of Cagliari, Salusio VI, was forced to flee and his giudicato was divided up between the victors: a third to Gallura, a third to Arborea, and a third to the Gherardeschi of Pisa.
Ogliastra and Sarrabus went to John Visconti of Gallura, while the curatori of Gippi, Nuraminis, Trexenta, Marmilla inferiore, Dolia, Gerrei, and Barbagia di Seulo went to Arborea.
Sulcis, Cixerri, Nora, and Decimo were granted to Gherardo and Ugolino della Gherardesca, counts of Donoratico, while Cagliari itself went to the commune of Pisa.