  In a LCDM cosmology, the Milky Way accretes satellites into the stellar disc.
We use cosmological simulations to assess the frequency of near disc plane and
higher inclination accretion events, and collisionless simulations of satellite
mergers to quantify the final state of the accreted material and the effect on
the thin disc. On average, a Milky Way-sized galaxy has 3 subhalos with
vmax>80km/s; 7 with vmax>60km/s; and 15 with vmax>40km/s merge at redshift z>1.
Assuming isotropic accretion, a third of these merge at an impact angle <20
degrees and are dragged into the disc plane by dynamical friction. Their
accreted stars and dark matter settle into a thick disc. The stellar thick disc
qualitatively reproduces the observed thick disc at the solar neighbourhood,
but is less massive by a factor ~2-10. The dark matter disc contributes 0.25-1
times the halo density at the solar position. Although not likely to be
dynamically interesting, the dark disc has important implications for the
direct detection of dark matter because of its low velocity with respect to the
Earth. Higher inclination encounters (>20 degrees) are twice as likely as low
inclination ones. These lead to structures that closely resemble the recently
discovered inner/outer stellar halos. They also do more damage to the Milky Way
stellar disc creating a more pronounced flare, and warp; both long-lived and
consistent with current observations. The most massive mergers (vmax>80km/s)
heat the thin disc enough to produce a thick disc. These heated thin disc stars
are essential for obtaining a thick disc as massive as that seen in the Milky
Way; they likely comprise some ~50-90% of the thick disc stars. The Milky Way
thin disc must reform from fresh gas after z=1 [abridged].
