  We characterise 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
halos. 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 ($z\gtrsim 4$), 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.
