Primordial black hole clusters evolve through successive mergers described by Smoluchowski coagulation — the same mathematical framework used for dust grains clumping in protoplanetary disks and droplets coalescing in clouds. Trashorras et al. (arXiv 2604.01684) show that under gravitationally focused conditions, these clusters undergo runaway growth: a single object captures most of the mass through a cascade of mergers. The timescale to runaway depends almost entirely on the initial mass distribution and the initial concentration of the cluster. Widely separated initial conditions lead to runaway on timescales differing by orders of magnitude. The final object may look similar — a massive black hole at the cluster center — but the path to it was set at formation.

Redirection networks (arXiv 2604.01540) grow by a different rule but show the same sensitivity. Instead of connecting to a randomly chosen target node, each new node connects to a neighbor of the target. This single indirection — attachment mediated through an existing connection — changes the network’s global structure. The number of nonleaf nodes scales sublinearly with network size. Most nodes remain leaves. A few early nodes accumulate connections not because they are intrinsically special but because they were present when the first redirections occurred. Their early position in the attachment sequence gave them a structural advantage that compounded.

In the black hole cluster, the first object to capture a neighbor gains a cross-section advantage — larger mass means larger gravitational focus, which means faster subsequent captures. In the redirection network, the first node to receive a redirected edge gains a degree advantage — more connections means higher probability of being a neighbor of future targets. Both are positive feedback loops seeded by initial conditions.

In both systems, the first attachment determines the trajectory, not the final size.