The international expansion of higher education has intensified in recent decades with a rapidly growing number of international branch campuses appearing on the scene. This study investigates the economic, cultural and institutional, and educational determinants of transnational higher education on both the extensive margin (number of international branch campuses), and the intensive margin (the total number of educational programmes offered). Using the gravity equation, we applied fixed-effect empirical methods to a panel dataset that combined and extended the raw data from campuses and master's programmes in 33 source countries and 76 host countries in the period from 1948 to 2016. Estimates reveal that although cultural, economic and institutional ties foster cross-border educational relationships, their effect differs significantly from one margin to another. The study highlights the relevance of globalisation, research activities, and aggregate demand in international higher education.