The morphology of nanocrystals serves as a powerful handle to modulate their functional properties. For semiconducting nanostructures, the shape is no less important than the size and composition, in terms of determining the electronic structure. For example, in the case of nanoplatelets (NPLs), their two-dimensional (2D) electronic structure and atomic precision along the axis of quantum confinement makes them well-suited as pure color emitters and optical gain media. In this study, we describe synthetic efforts to develop ZnSe NPLs emitting in the ultraviolet part of the spectrum. We focus on two populations of NPLs, the first having a sharp absorption onset at 345 nm and a previously unreported species with an absorption onset at 380 nm. Interestingly, we observe that the nanoplatelets are one step in a quantized reaction pathway that starts with (zero-dimensional (0D)) magic-sized clusters, then proceeds through the formation of (one-dimensional (1D)) nanowires toward the (2D) "345 nm" species of NPLs, which finally interconvert into the "380 nm" NPL species. We seek to rationalize this evolution of the morphology, in terms of a general free-energy landscape, which, under reaction control, allows for the isolation of well-defined structures, while thermodynamic control leads to the formation of three-dimensional (3D) nanocrystals.