  We use our state-of-the-art semi analytic model for GAlaxy Evolution and
Assembly (GAEA), and observational measurements of nearby galaxies to study the
influence of the environment on the gas content and gaseous/stellar disc sizes
of star-forming galaxies. We analyse the origin of differences between physical
properties of satellites and those of their central counterparts, identified by
matching the Vmax of their host haloes at the accretion time of the satellites.
Our model reproduces nicely the differences between centrals and satellites
measured for the HI mass, size of the star-forming region, and stellar radii.
In contrast, our model predicts larger differences with respect to data for the
molecular gas mass and star formation rate. By analysing the progenitors of
central and satellite model galaxies, we find that differences in the gas
content arise after accretion, and can be entirely ascribed to the
instantaneous stripping of the hot gas reservoir. The suppression of cold gas
replenishment via cooling and star formation leads to a reduction of the cold
gas and of its density. Therefore, more molecular gas is lost than lower
density HI gas, and model satellites have less molecular gas and lower star
formation rates than observed satellites. We argue that these disagreements
could be largely resolved with the inclusion of a proper treatment for
ram-pressure stripping of cold gas and a more gradual stripping of the hot gas
reservoir. A more sophisticated treatment of angular momentum exchanges,
accounting for the multi-phase nature of the gaseous disc is also required.
