  We use the Eagle simulation to study the relationship between the stellar
haloes of Milky-Way-mass galaxies and their recent merger histories. The
stellar mass ratio of the most massive merger that occurred since $z=1$ is
strongly correlated with the $z=0$ fraction of ex situ stars in the galaxy,
$f_{\rm ex\ situ}$, but is weakly correlated with stellar halo mass fraction,
$f_{\rm SH}$, particularly for disc galaxies. Contrary to common belief, our
results suggest that disc galaxies with low mass stellar haloes do not
necessarily have quiescent merger histories; in fact, roughly one quarter have
experienced a merger with stellar mass ratio $> 0.1$ since $z=1$. We
demonstrate that the population of disc galaxies with low $f_{\rm SH}$ and
active merger histories undergo mergers with satellites whose orbits are more
circular than average and are approximately co-planar with the disc; instead of
contributing significantly to the stellar halo, these mergers lead to discs
that contain a substantial fraction of ex situ stellar mass and are thicker and
more extended than those of quiescent galaxies. Such mergers also supply fuel
that often incites a significant episode of in situ star formation in the disc.
Our results suggest that seemingly quiescent disc galaxies with low-mass
stellar haloes actually have diverse merger histories, which limits the extent
to which stellar haloes alone can act as observable tracers of the hierarchical
assembly of galaxies.
