This paper examines the housing trajectories of complete cohorts of asylum migrants in Switzerland. It emphasizes the logistics of housing allocation by local authorities and how it shapes individual opportunity structure. We use full-population register data and analyse one key transition: the transition out of collective centre assigned upon arrival to the private and subsidized housing sectors. Event history models show the association between individual and contextual factors and the speed of access to private housing. Despite the quasi-autonomous management of refugee housing by region, priority rules regarding access to private housing were found to apply across the country. When choosing between different profiles, women, older asylum migrants, married individuals, and members of larger national groups are favoured in obtaining access to private housing. Nevertheless, the time spent in collective centres largely depends on the region to which a claimant is assigned, pointing to the minimal agency asylum migrants have during their first years of residence.