In social animals, morphological and behavioural traits may give to some individuals a stronger influence on the collective decisions, even in groups assumed to be leaderless such as fish shoals. Here, we studied and characterized the leadership in collective movements of shoals of zebrafish Danio rerio by observing groups of 2, 3, 5, 7 and 10 zebrafish swimming in a two resting sites arena during one hour. We quantified the number of collective departures initiated by each fish and the number of attempts that they made. To do so, we developed an automated pipeline that analysed the individual trajectories generated by the tracking software. For all shoal sizes, the leadership was distributed among several individuals. However, it was equally shared among all the fish in some shoals while other groups showed a more asymmetrical sharing of the initiation of collective departures. To quantify this distribution, we computed the entropy associated with the time series of the identity of all initiators for each experiment and confirmed the presence of a continuum between a homogeneous and a heterogeneous distribution of the leadership. While some fish led more departures than others, an individual analysis showed that all fish had actually the same success rate to lead the shoal out of a resting site after an attempt. Thus, some individuals monopolized the leadership by attempting more often than others to exit a resting site. Finally, we highlight that the intra-group ranking of a fish for the initiative is correlated to its intra-group ranking for the average speed with mobile individuals more prone to lead the shoal. These results demonstrate that the collective behaviour of a shoal can be mainly driven by a subset of individuals even in the absence of higher influence of a fish on its congeneers.