We perform the largest currently available set of direct N-body calculations of young star cluster models to study the dynamical influence, especially through the ejections of the most massive star in the cluster, on the current relation between the maximum stellar mass and the star cluster mass. We vary several initial parameters such as the initial half-mass radius of the cluster, the initial binary fraction and the degree of initial mass segregation. Two different pairing methods are used to construct massive binaries for more realistic initial conditions of massive binaries. We find that lower mass clusters () do not shoot out their heaviest star. In the case of massive clusters (), no most massive star escapes the cluster within 3 Myr regardless of the initial conditions if clusters have initial half-mass radii, r0.5, ≥0.8 pc. However, a few of the initially smaller sized clusters (r0.5= 0.3 pc), which have a higher density, eject their most massive star within 3 Myr. If clusters form with a compact size and their massive stars are born in a binary system with a mass ratio biased towards unity, the probability that the mass of the most massive star in the cluster changes due to the ejection of the initially most massive star can be as large as 20 per cent. Stellar collisions increase the maximum stellar mass in a large number of clusters when clusters are relatively dense ( and r0.5= 0.3 pc) and binary rich. Overall, we conclude that dynamical effects hardly influence the observational maximum stellar mass–cluster mass relation.