We propose a polymer model to investigate the dynamics of chromatin replication in three dimensions (PolyRep). Our results indicate that replication complexes, the replisomes, may self-assemble during the process and replicate chromatin by extruding it (immobile replisome) or by moving along the template filament (tracking replisome), reconciling previous discordant experimental evidence in favour of either scenario. Importantly, the emergence of one of the two morphologies depends in a major way on the replication origin distribution as well as on the presence of nonspecific interactions between unreplicated chromatin and firing factors—polymerases and other components of the replisome. Nonspecific interactions also appear instrumental to creating clusters of factors and replication forks, structures akin to the replication foci observed in mammalian cells . PolyRep simulations predict different mechanisms for foci evolution, including unanticipated loop-mediated fusion dynamics. We suggest that cluster formation, which our model suggests to be a generic feature of chromatin replication, provides a hitherto underappreciated but robust pathway to avoid stalled or faulty forks, which would otherwise diminish the efficiency of the replication process. Published by the American Physical Society 2024