The morphology diagram of possible structures in two-dimensional diffusional growth is given in the parameter space of undercooling Delta versus anisotropy of surface tension epsilon. The building block of the dendritic structure is a dendrite with a parabolic tip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. We show the analogy of diffusional growth with dewetting patterns of a fluid film on a substrate. We also describe the structures and velocities of fractal dendrites and doublons destroyed by noise. The extension of these results to three-dimensional growth is briefly discussed.