In the adult mammalian brain neural stem cells (NSCs) are considered rare cells restricted to two specialised niches, the subventricular zone (SVZ) and the subgranular zone. Recent findings demonstrated that in response to injury new neurons can be generated also by parenchymal astrocytes, however the prevalence, distribution, and behaviour of these ectopic NSCs remained elusive. Consequently, the extent to which the neurogenic potential of the mature brain parenchyma differs from that of conventional neurogenic niches remains to be determined. To tackle this issue, here, we reconstructed the spatio-temporal pattern of striatal astrocyte neurogenic activation after excitotoxic lesion in mice by employing lineage-tracing, clonal analyses, BrdU birth-dating and 3D-reconstructions coupled with mathematical modelling and spatial analyses. Our results indicate that the potential to initiate a neurogenic response is widely distributed in the striatum but is focally activated at the lesion border. In this region, astrocytes enter a neurogenically active state at a constant rate but in random locations, generating independent neurogenic foci that expand for about 10 days. Activated astrocytes quickly came back to quiescence, while their progeny composed of TAPs-like cells and immature neurons transiently proliferated, following a stochastic behaviour that features an acceleration in differentiation propensity. Interestingly the fraction of astrocytes undergoing neurogenic activation at any given time matches that of SVZ astrocytes indicating that the prevalence of NSC potential among striatal astrocytes is comparable to that in canonical niches. These results challenge the view that NSCs are a rare and anatomically restricted cell population in the adult brain.