The paper returns to a long-standing issue in the literature on higher education systems, that of the relationship, if any, between diversity (horizontal differentiation based on variation in HEI mission, organisational cultures, educational practices etc), the growth of participation levels, and marketisation. The classical American literature suggested that diversity, participation and competition all tended to advance together but more recent empirical studies in the English-speaking world suggest that markets foster vertical differentiation rather than horizontal variety and encourage imitating behaviour which reduces diversity, while the growth of participation is neutral in relation to horizontal diversity. States have contrary implications for diversity: sometimes they regulate greater homogenisation, sometimes they deliberately foster variety in the form of specialist institutions or sectors. The paper surveys the world wide terrain, in which participation is rapidly advancing—in 56 countries more than 50% of the young age cohort enters higher education. It finds that the principal features of the present period, in association with growth, are (1) the advance of the multi-purpose multi-disciplinary research multiversity as the main institutional form, (2) a secular decline in the role of non-university sectors and specialist institutions , (3) an increase in internal diversity in the large multiversities, (4) an increase in vertical stratification in many systems, (5) no increase in horizontal diversity overall and a probable decline in diversity, except for the rise of for-profit colleges in some countries.