ABSTRACT By means of three-dimensional hydrodynamical simulations, we investigate the formation of second-generation (SG) stars in young globular clusters of different masses. We consider clusters with a first generation of asymptotic giant branch (AGB) stars with mass 105 and $10^6\, \mathrm{M}_{\odot }$ moving at constant velocity through a uniform gas with density 10−24 and 10−23 g cm−3. Our set-up is designed to reproduce the encounter of a young cluster with a reservoir of dense gas, e.g. during its orbital motion in the host galaxy. In the low-density models, as a result of the cooling AGB ejecta which collect in the centre, weakly perturbed by the external ram pressure, a compact central He-rich SG stellar component is formed on a time-scale which decreases with increasing initial cluster mass. Our high-density models are subject to stronger ram pressure, which prevents the accumulation of the most He-rich AGB ejecta in the cluster centre. As a result, the SG is more extended and less He-enhanced than in the low-density models. By combining our results with previous simulations, we are able to study relevant, cluster-related scaling relations across a dynamical range of two orders of magnitude in mass (from $10^5 $ to $10^7 \, \mathrm{M}_{\odot }$). In agreement with current observationally based estimates, we find positive correlations between the SG-to-total number ratio and maximum He enhancement in SG stars as a function of the initial cluster mass.