Predicting whether higher education systems will lead to wider and more equitable participation calls for multiple perspectives going outside the European and Anglophone worlds, and beyond looking education also to other sub-systems of society and government. This reminds us to consider need as well as supply and demand, the importance of place and regions, and the new salience of "engagement", as well as the vital importance of different cultural contexts for what they determine and allow for universalising higher education systems. More or less deep-reaching curriculum changes may occur. Seven different possible models for the future of HE are proposed, concluding with a prognosis as to what scenario is likely to prevail.