We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two dimensions, and the deposition front, or growth line, varies spatiotemporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson-like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by Kardar-Parisi-Zhang fluctuations in the presence of quenched disorder.