I use a library of controlled minor merger N-body simulations, a particle tagging technique and Monte Carlo generated ΛCDM 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).