Contrary to the overall tendency to increase student participation in the financing of higher education, Estonia abolished student tuition fees in 2013. We study the effects of this reform on the students' access to and progress in higher education, concentrating mostly on the changes in probabilities of rural and remote students being admitted (extensive margin) and graduating within a nominal time (intensive margin). We distinguish between four different outcomes: admission in general, admission to vocational education, admission to high-rank curricula, and graduation within nominal time. We confirm the tendency that a high socioeconomic status increases the probability of being admitted to high-rank curricula and reduces the probability of choosing an applied curriculum, and the 2013 reform did not change that. While the reform weakly improved rural students' tendency to graduate on time, it diminished the probability that they were admitted to high-rank curricula. So, paradoxically and contrary to the intention of the reform, higher state involvement in higher education financing has not improved the equity in university admission in Estonia in terms of either socioeconomic background or regional disparities. We claim that part of the explanation of that paradox lies in the conditionality of this reform and the combination of a scarce needs-based and a competitive merit-based student support system in Estonia. We see our broader contribution in emphasising the important role of support systems in the future analysis of the potential to improve students' access.