Abstract We present the findings of a comprehensive and detailed analysis of merger tree data from ultra-high-resolution cosmological $N$-body simulations. The analysis, conducted with a particle mass resolution of $5 \times 10^3 h^{-1} M_{\odot}$ and a halo mass resolution of $10^7 h^{-1} M_{\odot}$, provides sufficient accuracy to suppress numerical artefacts....