In this paper, we provide a comprehensive picture of social selectivity in higher education in Italy by focusing on enrolment and two alternative indicators of success: retention and timely completion. The existing literature has shown that young individuals of disadvantaged backgrounds have lower enrolment probabilities and higher chances of withdrawal. This paper analyses the size and features of this cumulative disadvantage, shaping the chances of high-school leavers of eventually attaining the university degree. We analyse whether social background inequalities are stronger at enrolment or at later outcomes, and how these inequalities vary with previous schooling experience. We confirm previous evidence that disadvantaged groups with respect to enrolment are also disadvantaged on persistence, add new findings on timely completion and show that cumulative inequalities are very strong. Inequalities are strongest among students holding technical and vocational high-school qualifications and weakest among well-performing students from lyceums. In addition, we examine the role of labour market conditions and whether they explain geographical differences. Enrolment, retention and timely completion probabilities appear negatively related to local youth unemployment rates, suggesting that with poor labour market prospects, individuals lose motivation and reduce their engagement in education.