Merger tree showing the evolution of the dark-matter smooth accretion. We only show the fifty most massive branches. The junctions with less massive branches are indicated with small arrowheads. The main branch (on the left) is built up through a smooth accretion process Ṁ_acc (Eq. (1)) and multiple mergers with other haloes. The evolution of the smooth dark-matter accretion through the merger tree is shown with colour. A halo without any dark-matter accretion is shown with a black symbol. Circles are used for main haloes (M-H), while squares are used for subhaloes (S-H). The size of the symbols is proportional to the dark-matter halo virial mass. It is clearly visible that before a merger event with a larger structure, a halo is systematically identified as a substructure of this more massive halo. During this subhalo phase, the dark-matter accretion rate strongly decreases and may even stop.