Some lineages radiate spectacularly when colonising a region, but others do not. Large radiations are often attributed to species’ adaptation into niches, but sometimes instead to other drivers, such as biogeography. Here we aim to disentangle the factors determining radiation size, by modelling simplified scenarios without the complexity of explicit niches. We build a spatially structured neutral model free from niches and incorporating a form of protracted speciation that accounts for gene flow between populations. We characterise the behaviour of the model for a range of different networks of connectivity between patches. We find that a wide range of radiation sizes are possible depending on the combination of geographic isolation and species' dispersal ability. For example, when considering isolated archipelagos, low rates of dispersal from the mainland result in decreased competition and thus increased radiation size. Dispersal between habitat patches also has an important effect. At extremely low dispersal rates, each habitat patch has its own endemic species, intermediate dispersal rates foster larger radiations. As dispersal rates increase further, a critical point is reached at which identical lineages can vary greatly in radiation size due to rare and stochastic dispersal events. At the critical point, some lineages remain a single species for a long time, whilst others with identical characteristics produce the largest radiations of all. The mechanism for this is a ‘radiation cascade’ in which speciation leads to reduced numbers of individuals per species, and thus reduced gene flow between conspecifics in isolated patches, leading to yet more speciation. Once a radiation cascade begins, it continues rapidly until it is arrested by a new equilibrium between speciation and extinction. We speculate that such cascades may occur more generally and are not only present in neutral models. This may help to explain rapid radiation, and the extreme radiation sizes of certain lineages. Whilst niches no doubt play a role in community assembly, our findings lead us to question if diversification and adaptation into niches is sometimes an effect of speciation and rapid radiation, rather than its cause.