The inner boundary of protoplanetary discs is structured by the dramatic opacity changes at the transition from the dust-containing toa dust-free zone. This paper explores the variety and limits of inner rim structures in passively heated dusty discs. For this study, weimplemented detailed sublimation physics in a fast Monte Carlo radiative transfer code. We show that the inner rim in dusty discs isnot an infinitely sharp wall but a diffuse region which may be narrow or wide. Furthermore, high surface densities and large silicategrains as well as iron and corundum grains decrease the rim radius, from a 2.2 AU radius for small silicates around a 47 L_⊙Herbig Aestar typically to 0.4 AU and as close as 0.2 AU. A passive disc with grain growth and a diverse dust composition must thus have a smallinner rim radius. Finally, an analytical expression is presented for the rim location as a function of dust, disc and stellar properties.
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