  In a recent contribution, Bahl \& Baumgardt investigated the incidence of
planar alignments of satellite galaxies in the Millennium-II simulation, and
concluded that vast thin planes of dwarf galaxies, similar to that observed in
the Andromeda galaxy (M31), occur frequently by chance in $\Lambda$-Cold Dark
Matter cosmology. However, their analysis did not capture the essential fact
that the observed alignment is simultaneously radially extended, yet thin, and
kinematically unusual. With the caveat that the Millennium-II simulation may
not have sufficient mass resolution to identify confidently simulacra of
low-luminosity dwarf galaxies, we re-examine that simulation for planar
structures, using the same method as employed by Ibata et al. (2013) on the
real M31 satellites. We find that 0.04\% of host galaxies display satellite
alignments that are at least as extreme as the observations, when we consider
their extent, thickness and number of members rotating in the same sense. We
further investigate the angular momentum properties of the co-planar
satellites, and find that the median of the specific angular momentum derived
from the line of sight velocities in the real M31 structure ($1.3\times10^4$
km/s kpc) is very high compared to systems drawn from the simulations. This
analysis confirms that it is highly unlikely that the observed structure around
the Andromeda galaxy is due to a chance occurrence. Interestingly, the few
extreme systems that are similar to M31 arise from the accretion of a massive
sub-halo with its own spatially-concentrated entourage of orphan satellites.
