Welfare reforms introduced at national level and implying changes in service provision are often managed by local authorities, and this fact paves the way for strong local‐central tensions. One of the sources of such tensions is the spread of local discretion in the implementation of central programs. In current literature, local discretion has been considered as a way not only to preserve local autonomy but also to capture central resources or to shift cost burdens upwards. This opportunistic behaviour is especially spread in countries characterized by weak vertical coordination in their multi‐level governance system. This paper investigates the dynamics of local discretion as a specific phenomenon relating to central‐local tensions by observing the implementation of an innovative national long‐term care program (Home Care Premium), in a national context (Italy) characterized by a high degree of institutional fragmentation. The findings show that, in spite of the programme's centralistic orientation and generous funding, specific discretionary practices have been extensively adopted by local authorities to develop strategies aimed at shifting the costs of local service provision towards central funding. Using a specific measure of local discretion, we examine first the territorial distribution of discretion over the country. Then, a regression model is developed to explain to what extent local discretion is explained by demand‐side, supply‐side or policy legacy factors. Results show the relevance of territorial socio‐economic inequalities in explaining local discretion and related cost‐shifting behaviours by local authorities located in poorest, highly deprived areas.