  We report the alignment and shape of dark matter, stellar, and hot gas
distributions in the EAGLE and cosmo-OWLS simulations. The combination of these
state-of-the-art hydro-cosmological simulations enables us to span four orders
of magnitude in halo mass ($11 < log_{10}(M_{200}/ [h^{-1}M_\odot]) < 15$), a
wide radial range ($-2.3 < log_{10}(r/[h^{-1}Mpc ]) < 1.3$) and redshifts $0 <
z < 1$. The shape parameters of the dark matter, stellar and hot gas
distributions follow qualitatively similar trends: they become more aspherical
(and triaxial) with increasing halo mass, radius and redshift. We measure the
misalignment of the baryonic components (hot gas and stars) of galaxies with
their host halo as a function of halo mass, radius, redshift, and galaxy type
(centrals vs satellites and early- vs late-type). Overall, galaxies align well
with the local distribution of the total (mostly dark) matter. However, the
stellar distributions on galactic scales exhibit a median misalignment of about
45-50 degrees with respect to their host haloes. This misalignment is reduced
to 25-30 degrees in the most massive haloes ($13 < log_{10}(M_{200}/
[h^{-1}M_\odot ]) < 15$). Half of the disc galaxies in the EAGLE simulations
have a misalignment angle with respect to their host haloes larger than 40
degrees. We present fitting functions and tabulated values for the probability
distribution of galaxy-halo misalignment to enable a straightforward inclusion
of our results into models of galaxy formations based on purely collisionless
N-body simulations.
