Left panel: initial cluster mass and half-mass radius for YCs (bottom left area), GCs (central area), and NSCs (upper right area). The cluster distributions are cut at the 99% contour. Clusters with t_cc < 5 Myr lie below the dot-dashed black line; those with central density ρ_cl,0 > 10⁵ M_⊙ pc⁻³ are above the shaded dotted gray line. We also identify regions of the parameter space in which (i) a BBH binary is ejected before merging due to strong Newtonian recoils (in pink), (ii) the merger remnant is typically kicked out of the cluster due to its relativistic kick (in purple), (iii) the BBH merger time exceeds a Hubble time (in yellow). Right panel: schematic overview of a BH dynamical growth in a star cluster. The colored boxes refer to the regions highlighted in the left plot.