  We present six simulations of galactic stellar haloes formed by the tidal
disruption of accreted dwarf galaxies in a fully cosmological setting. Our
model is based on the Aquarius project, a suite of high resolution N-body
simulations of individual dark matter haloes. We tag subsets of particles in
these simulations with stellar populations predicted by the Galform
semi-analytic model. Our method self-consistently tracks the dynamical
evolution and disruption of satellites from high redshift. The luminosity
function and structural properties of surviving satellites, which agree well
with observations, suggest that this technique is appropriate. We find that
accreted stellar haloes are assembled between 1<z<7 from less than 5
significant progenitors. These progenitors are old, metal-rich satellites with
stellar masses similar to the brightest Milky Way dwarf spheroidals. In
contrast to previous stellar halo simulations, we find that several of these
major contributors survive as self-bound systems to the present day. Both the
number of these significant progenitors and their infall times are inherently
stochastic. This results in great diversity among our stellar haloes, which
amplifies small differences between the formation histories of their dark halo
hosts. The masses and density/surface-brightness profiles of the stellar haloes
are consistent with expectations from the Milky Way and M31. Each halo has a
complex structure, consisting of well-mixed components, tidal streams, shells
and other subcomponents. This structure is not adequately described by smooth
models. We find one example of an accreted thick disk. Contrasts in age and
metallicity between halo stars and those in surviving satellites are in broad
agreement with recent observations. [Abridged]
