We look at the expansion of a higher education system through the lens of concentration in the distribution of enrollments among institutions. Using data from the Brazilian Higher Education Censuses from 2002 to 2016, we found that the diversification of segments that compose the system was associated with an increase in concentration and market oligopolization. The higher education expansion in Brazil has a history of high growth and high concentration among large institutions. Enrollment more than doubled in 14 years, but growth among the top 1% of institutions was higher than the total growth among the bottom 90% of institutions. Much of the market concentration was due to a combination of subsidized privatization and deregulated virtualization. Private distance education was the main driver of concentration. By the end of the 2002-2016 period, the private sector contributed to 77% of all concentration, with private distance education alone contributing to 40%.