Well-behaved assembly histories for all mass components of the halo identified as FoFID 28000000000013. We plot M_200c as a solid black line with crosses, M_* as a solid salmon line with “×”-shaped markers, and M_BH as a solid red line with small diamonds. The corresponding curve fit functions are shown as dashed lines with coloured dots (blue for M_200c, yellow for M_*, and light grey for M_BH). The horizontal black dashed lines represent t_50% and t_70%. We observe that these histories display discrete behaviour with some degree of discontinuity. Using methods like curve fitting could result in significantly different estimates for the half-mass assembly time, which we aim to avoid. This example demonstrates that the interpolation approach, without any fit, provides a more accurate result.