The article asks for the aim of Pope Alexander VI around the so-called Alexandrian bulls. Our purpose is to prove that the Pope did not act as an arbitrator about the Iberian disputes given that he always acted from his capital position as Vicar of Christ and supported by the Medieval cannonists’ doctrine about Lordship of the World. Four aspects are analysed: the historians’ views; the position of Christian princes to conquer territories inhabited by infidels; pontifical action motu proprio according to canon law; and the expendable intervention according to the circumstantial convenience of the Portuguese and Castilian Crowns.