The evolution of crystal growth morphologies was explored using a Monte Carlo model. The model combines diffusive transport in the nutrient with thermally activated and local configuration-dependent steps for attachment, surface diffusion and detachment. The solid pair interaction energy, φ, temperature, T, and chemical potential difference between nutrient and surface, Δμ, were used as input parameters. For a given set of simulation parameters, we found that, due to the competing effects of bulk diffusion and interface kinetics, there is a critical size beyond which a crystal cannot retain its macroscopically faceted shape. This critical size scales linearly with the mean free path in the nutrient, a. The stabilization of the growth shape by anisotropies in the kinetics is reduced through thermal and kinetic roughening. Thus, further increases either in T or Δμ, and/or decreases in φ, cause successive transitions from faceted to compact dendritic and side-branched dendritic morphologies. On interfaces with emerging screw dislocations the spiral growth mechanism dominates at low Δμ. When a is comparable to the lattice constant, the combination of bulk and surface diffusion reduces the terrace width near the centre of a growth spiral. At elevated T and Δμ, 2D nucleation-controlled growth can dominate in the more readily supplied corner and edge regions of a facet, while spiral growth prevails in its centre.