Models of deposition and detachment dynamics of different shaped anisotropic colloids are reported to understand how equilibrium deposited amounts compare to spherical colloids. For different shaped colloids including spheres, ellipsoids, toroids, and buckled particles with varying aspect ratios, interaction potentials with substrates are computed using the Derjaguin approximation. Using these potentials, the Smoluchowski equation is used to model the dynamics of deposition and detachment versus particle-substrate attraction and aspect ratio for each particle shape. Average times for deposition and detachment and their ratio show steady-state deposited amounts can be enhanced by several orders of magnitude for different particle shapes compared to spherical colloids of the same volume. From a mechanistic standpoint, the present findings indicate how local Gaussian curvature of different particle shapes can lead to stronger adhesive interactions, longer detachment times, and higher deposited amounts compared to spherical colloids, which provides general design rules for controlling and optimizing colloidal deposition.