Abstract: The article explains the so-called ‘omni-insular’ theory based on the donation of Constantine. We conclude that the references to this Donation are few and circumstantial. Just in some cases can be testified that the Pope demanded an economical and periodical amount based on his rights over the whole Occident islands. This amount seems derived from the feudal context, the prestige of being the successor of Peter, and the recognition of apostolic protection. The intervention of the popes in the Portuguese and Castilian overseas expansion was based firstly on their condition of Vicar of Christ (apostolic authority) and secondly on the hierocratic doctrine of the Lordship of the World (Dominium Mundi). Key Words: Papacy, omni-insular theory, apostolic authority.Resumen: El artículo expone la teoría omni-insular fundada en la donación de Constantino. Se concluye que: las menciones a la donación son muy pocas y circunstanciales; si el Papa exigió un censo basado en que tenía potestad sobre todas las islas de Occidente está probado en algunos casos, pero no en todos; el censo parece explicarse por el contexto feudal, el prestigio de ser el sucesor de Pedro y el reconocimiento de la protección apostólica; la intervención de los papas en la expansión ultramarina portuguesa y castellana se funda, primero, en su condición de Vicario de Cristo (potestad apostólica), y segundo, en la doctrina hierocrática del Señorío del Mundo (Dominium Mundi). Palabras clave: Papado, teoría omni-insular, potestad apostólica. Abstract: The article explains the so-called ‘omni-insular’ theory based on the donation of Constantine. We conclude that the references to this Donation are few and circumstantial. Just in some cases can be testified that the Pope demanded an economical and periodical amount based on his rights over the whole Occident islands. This amount seems derived from the feudal context, the prestige of being the successor of Peter, and the recognition of apostolic protection. The intervention of the popes in the Portuguese and Castilian overseas expansion was based firstly on their condition of Vicar of Christ (apostolic authority) and secondly on the hierocratic doctrine of the Lordship of the World (Dominium Mundi). Key Words: Papacy, omni-insular theory, apostolic authority. *El artículo es parte de una investigación titulada “El fin del Papado medieval. El Papado ante Portugal y Castilla por el dominio del Atlántico (siglos xiv y xv)”, financiada por la Vicerrectoría de Investigación, Innovación y Postgrado de la Universidad del Bío-Bío, DIUBB 183224 4/R 2018-2019.