The interaction of the Milky Way (MW) satellite galaxies with the Galactic environment produces tidal tails that are observed as denser concentrations in the sky (e.g. like in the case of the Magellanic Clouds tails or the Sagittarius dwarf stream). In this work we address via numerical simulations the distribution of dark matter (DM) and baryonic tidal streams in the Milky Way environment. We model our initial conditions (ICs) according to the Aquarius A2-to-F2 simulations and previous literature, employing satellite models made both of baryons and DM. We find that most of the baryons are still inside their progenitors, while most of DM is easily stripped and redistributed in the MW environment. We also find that the stripped baryonic debris ends up mostly in the inner regions of the MW halo and that it is flatter than the DM debris. A look at the angular distribution of the debris shows that it is oriented at specific angles with respect to the Galactic disk. This is found also rotating the satellites of 90 degrees with respect to their previous positions and running the simulations again. This result surprisingly contrasts with the expectations of a randomly distributed debris. Next, we move to extract ICs from latest cosmological simulations and to switch on gas dynamics and feedback to study the impact of baryonic physics on the distribution of satellite debris in the MW environment.