ABSTRACT We characterize the population of wandering black holes, defined as those physically offset from their halo centres, in the romulus cosmological simulations. Unlike most other currently available cosmological simulations, black holes are seeded based on local gas properties and are permitted to evolve dynamically without being fixed at halo centres. Tracking these black holes allows us to make robust predictions about the offset population. We find that the number of wandering black holes scales roughly linearly with the halo mass, such that we expect thousands of wandering black holes in galaxy cluster haloes. Locally, these wanderers account for around 10 per cent of the local black hole mass budget once seed masses are accounted for. Yet for higher redshifts ($z$ ≳ 4), wandering black holes both outweigh and outshine their central supermassive counterparts. Most wandering black holes, we find, remain close to the seed mass and originate from the centres of previously disrupted satellite galaxies. While most do not retain a resolved stellar counterpart, those that do are situated farther out at larger fractions of the virial radius. Wanderers with higher luminosities are preferentially at lower radius, more massive, and either closer to their host’s mid-planes or associated with a stellar overdensity. This analysis shows that our current census of supermassive black holes is incomplete and that a substantial population of off-centre wanderers likely exists.