The adjustment of services of general interest to ageing and shrinking populations is a significant challenge in many European regions. This article analyses the response in the number of primary schools to changes in the student population in the municipalities of mainland Portugal between 2007 and 2016. It focuses on the time lag of this adjustment, the territorial factors that influence it and the role of spatial spill-over effects. The main finding is that the relationship between the number of schools and the number of students is not straightforward and can only be understood considering the broader geographic contexts and spatial dependence structures.