Final 3D density profiles of the clumps in the spherical-host simulations presented in Sect. 5.1 (first two rows) and for the case in which the external potential also includes a Sparkler-like stellar disc as described in Sect. 5.2 (last two rows). First and third row: Clumps with mass 10^6.3 M_⊙, 10^6.6 M_⊙, and 10^6.9 M_⊙ (left, central, and right panels, respectively). Second and fourth row: Clumps with mass 10^7.2 M_⊙, 10^7.5 M_⊙, and 10^7.8 M_⊙ (left, central, and right panels, respectively). The black dots are the N-body density profiles, while the red solid line is the best-fit Plummer density profile (with the shaded are marking the 1σ, 2σ, and 3σ confidence levels), as described in Appendix A. The grey shaded area highlights the region within the softening length, that is excluded from the fit. The grey dashed line is the initial Plummer scale radius r_s, i, and the red dashed line is the best-fit final scale radius r_s, f.