Context :

Aims : We study the distribution of the Milky Way satellites stellar and dark matter debris .

Methods : For the first time we address the question of the tidal disruption of satellites in simulations by utilising simultaneously a ) a realistic set of orbits extracted from cosmological simulations , b ) a three component host galaxy with live halo , disc and bulge components , and c ) satellites from hydrodynamical simulations .
We analyse the statistical properties of the satellite debris of all massive galaxies reaching the inner Milky Way on a timescale of 2 Gyr .

Results : Up to 80 % of the dark matter is stripped from the satellites , while this happens for up to 30 % of their stars .
The stellar debris ends mostly in the inner Milky Way halo , whereas the dark matter debris shows a flat mass distribution over the full main halo .
The dark matter debris follows a density profile with inner power law index \alpha _ { DM } = -0.66 and outer index \beta _ { DM } = 2.94 , while for stars \alpha _ { * } = -0.44 and \beta _ { * } = 6.17 .
In the inner 25 kpc , the distribution of the stellar debris is flatter than that of the dark matter debris and the orientations of their short axes differ significantly .
Changing the orientation of the stellar disc by 90 ^ { o } has only a minor impact on the distribution of the satellite debris .

Conclusions : Our results indicate that the dark matter is more easily stripped than stars from the Milky Way satellites .
The structure of the debris is dominated by the satellite orbital properties .
The radial profiles , the flattening and the orientation of the stellar and dark matter debris are significantly different , which prevents the prediction of the dark matter distribution from the observed stellar component .