  We use the very high resolution, fully cosmological simulations from the
Aquarius project, coupled to a semi-analytical model of galaxy formation, to
study the phase-space distribution of halo stars in "solar neighbourhood"-like
volumes. We find that this distribution is very rich in substructure in the
form of stellar streams for all five stellar haloes we have analysed. These
streams can be easily identified in velocity space, as well as in spaces of
pseudo-conserved quantities such as E vs. Lz. In our best-resolved local
volumes, the number of identified streams ranges from ~ 300 to 600, in very
good agreement with previous analytical predictions, even in the presence of
chaotic mixing. The fraction of particles linked to (massive) stellar streams
in these volumes can be as large as 84%. The number of identified streams is
found to decrease as a power-law with galactocentric radius. We show that the
strongest limitation to the quantification of substructure in our
poorest-resolved local volumes is particle resolution rather than strong
diffusion due to chaotic mixing.
