  Using the 100-m radio telescope at Effelsberg, we mapped a large area around
the Andromeda Galaxy in the 21-cm line emission of neutral hydrogen to search
for high-velocity clouds (HVCs) out to large projected distances in excess of
100 kpc. Our 3-sigma HI mass sensitivity for the warm neutral medium is 8x10^4
solar masses. We can confirm the existence of a population of HVCs with typical
HI masses of a few times 10^5 solar masses near the disc of M31. However, we
did not detect any HVCs beyond a projected distance of about 50 kpc from M31,
suggesting that HVCs are generally found in proximity of large spiral galaxies
at typical distances of a few 10 kpc. Comparison with CDM-based models and
simulations suggests that only a few of the detected HVCs could be associated
with primordial dark-matter satellites, whereas others are most likely the
result of tidal stripping. The lack of clouds beyond a projected distance of 50
kpc from M31 is also in conflict with the predictions of recent CDM structure
formation simulations. A possible solution to this problem could be ionisation
of the HVCs as a result of decreasing pressure of the ambient coronal gas at
larger distances from M31. A consequence of this scenario would be the presence
of hundreds of mainly ionised or pure dark-matter satellites around large
spiral galaxies like the Milky Way and M31.
