  The inner boundary of protoplanetary discs is structured by the dramatic
opacity changes at the transition from the dust-containing to a dust-free zone.
This paper explores the variety and limits of inner rim structures in passively
heated dusty discs. For this study, we implemented detailed sublimation physics
in a fast Monte Carlo radiative transfer code. We show that the inner rim in
dusty discs is not an infinitely sharp wall but a diffuse region which may be
narrow or wide. Furthermore, high surface densities and large silicate grains
as well as iron and corundum grains decrease the rim radius, from a 2.2AU
radius for small silicates around a 47 Solar luminosity Herbig Ae star
typically to 0.4AU and as close as 0.2AU. A passive disc with grain growth and
a diverse dust composition must thus have a small inner rim radius. Finally, an
analytical expression is presented for the rim location as a function of dust,
disc and stellar properties.
