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One of the most expected benefits from the diffusion of car sharing services in urban areas is the decrease of car ownership levels and related impacts in terms of vehicle miles travelled, greenhouse gas emissions, and space consumption. Unlike previous studies in which the effects on public spaces are related to a reduced number of private vehicles, in this paper we present a method to analyse the spatial variation in parking demand in a city with the joint consideration of the kind of parking actually in use. A distinction is made between dedicated parking areas from on-street parking. A trip-level analysis approach is then followed, where car ownership is an exogenous variable and modelling scenarios on modal diversion patterns for different origin-destination pairs are examined. Travel demand models are calibrated and validated on a stated-preferences travel survey carried out in Turin in 2016 and applied on a revealed-preferences travel survey distributed in the cities of Milan and Turin (Italy) in May 2019. Both surveys were administered to a representative sample of the population living in the cities, therefore results can be generalised. The ideal scenario resulting from modal diversion patterns show that free-floating car sharing might produce positive and negative impacts on both on-street and on-surface dedicated parking areas. In particular, more positive impacts are expected on daily parking events in central areas, where mobility attractors are concentrated. On the contrary, higher negative impacts on both on-street and dedicated parking events might be encountered in more peripheral areas. [ABSTRACT FROM AUTHOR]