Fraction of events of the analyzed O1–O4a BH mergers retained in dense environments. We show the posterior distributions for O1–O4a fraction ﹩{\zeta }_{| {K}_{a}| \lt {v}_{{\rm{esc}}}}﹩ of events with a component of the final recoil along the final BH spin ∣K_a∣ is smaller than a given escape velocity v_esc. We consider v_esc = 50 km s⁻¹ for GCs (solid) and v_esc = 1000 km s⁻¹ for NSCs (dashed). Blue and orange lines correspond to O1–O3 and O1–O4a events, respectively. The prior distribution is uniform in [0, 1]. Since our calculation only considers the component of the recoil along the spin direction, our results represent upper bounds on the true fraction of retained remnants.