The article presents an extension of the theory of planned behaviour (TPB) to identify, in a Latin American university, the students who are children of entrepreneurial parents and the determinants of their willingness to succeed them. The TPB is used as a basis to analyse the intention to be a successor, and three constructs are added: affective commitment, normative commitment and parental role model. The analysis is carried out using structural equations via the partial least squares (PLS) method, which allows for the study of multiple relationships between construct-type variables. The sample includes 16,185 Latin American university students from the Global University Entrepreneurial Spirit Students’ Survey 2018 database. The results show that, in Latin American students, the determining factors in the intention to be a successor are attitude, the affective and normative commitment and the parental role model. The latter has a negative and significant effect on the intention to be a successor in the family business. One of the practical implications of this study has to do with the development of an affective feeling of the offspring towards the family business. Generating this kind of attachment since childhood could lead to achieving a greater relevance of the parental role model and a stronger interest in the succession of the business.