  I use a library of controlled minor merger N-body simulations, a particle
tagging technique and Monte Carlo generated $\Lambda$CDM accretion histories to
study the highly stochastic process of stellar deposition onto the accreted
stellar halos (ASHs) of $L_*$ galaxies. I explore the main physical mechanisms
that drive the connection between the accretion history and the density profile
of the ASH. I find that: i) through dynamical friction, more massive satellites
are more effective at delivering their stars deeper into the host; ii) as a
consequence, ASHs feature a negative gradient between radius and the local
mass-weighed virial satellite-to-host mass ratio; iii) in $L_*$ galaxies, most
ASHs feature a density profile that steepens towards sharper logarithmic slopes
at increasing radii, though with significant halo-to-halo scatter; iv) the ASHs
with the largest total ex-situ mass are such because of the chance accretion of
a small number of massive satellites (rather than of a large number of low-mass
ones).
