We present a comprehensive study of the distribution of matter around different populations of filaments, using the IllustrisTNG simulation at z=0. We compute the dark matter (DM), gas, and stellar radial density profiles of filaments, and we characterise the distribution of the baryon fraction in these structures. We find that baryons exactly follow the underlying DM distribution only down to r~7 Mpc to the filament spines. At shorter distances (r<7 Mpc) the baryon fraction profile of filaments departs from the cosmic value Omega_b/Omega_m. While in the r~0.7 - 7 Mpc radial domain this departure is due to the radial accretion of WHIM gas towards the filament cores (creating an excess of baryons with respect to the cosmic fraction), the cores of filaments (r<0.7 Mpc) show instead a clear baryon depletion, quantified by a depletion factor of Y_b = 0.63-0.68. The analysis of the efficiency of AGN feedback events in filaments reveals that they are potentially powerful enough to eject gas outside of the gravitational potential wells of filaments. We show that the large-scale environment (i.e. denser vs less-dense, hotter vs colder regions) has a non-negligible effect on the absolute values of the DM, gas, and stellar densities around filaments. Nevertheless, the relative distribution of baryons with respect to the underlying DM density field is found to be independent from the filament population. Finally, we provide scaling relations between gas density, temperature, and pressure for the different populations of cosmic filaments. We compare these relations to those pertaining to clusters of galaxies, and find that these cosmic structures occupy separate regions of the density-temperature and density-pressure planes.
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