We study the formation of colloidal CdSe nanoplatelets using both tansmission electron microscopy (TEM) and spectroscopic analysis. We show that the platelets form by continuous lateral extension of small (<2 nm) nanocrystal CdSe seeds. The nanoplatelet thickness is fixed by the seed dimension and remains constant during the platelet formation. The nanoplatelet lateral dimensions can be tuned using additional precursor injection. Absorption and fluorescence analysis of the CdSe nanoplatelets as they continuously extend laterally confirms a continuous transition from 3D to 1D confined nanoparticles. The formation of the CdSe platelets is found to be similar for different platelet thicknesses that we control with a precision of one CdSe monolayer.