Evolution of the proto-cluster radius in comoving and physical units scaled to r₂₀₀ at z = 0. Results for three cosmological models are shown by red lines (reference model), blue lines (Millennium cosmology) and dashed black lines (Planck cosmology). The over-plotted black dots show the parameterised approximation of r_com (see Eq. (2)) for the reference cosmology and r_phys for the Millennium cosmology.