With few exceptions, polydispersity or molecular heterogeneity in matter tends to impede selfassembly and state transformation 1-3. Here we report shape transition studies of nematic liquid crystal oligomer (NLCO) drops, which reveal, surprisingly, that molecular heterogeneity in the drops promotes reversible transitions to a rich variety of non-spherical morphologies with unique internal structure. Previously, shape transitions of homogeneous liquid drops with monodisperse ingredients have been reported in equilibrium 4-7 and non-equilibrium studies 8, 9 , with the latter producing filaments at active interfaces, albeit randomly without control. Our experiments employ equilibrium suspensions of drops composed of polydisperse NLCOs. Variation of oligomer chain length distribution, temperature, and surfactant concentration alters the balance between NLCO elastic energy and interfacial energy and drives formation of visually striking nematic structures ranging from roughened spheres to flowers to branched filamentous networks with controllable diameters. The branched structures with confined LC director fields can be produced reversibly over centimeter areas and converted into LC elastomers by UV curing. Remarkably, observations and modeling reveal that chain length polydispersity plays a crucial role in driving these morphogenic phenomena, via spatial segregation. This insight suggests new routes for encoding network structure and function in soft materials. We study NLCO drops, tens of microns in diameter, dispersed in water containing sodium dodecyl sulfate (SDS) surfactant. SDS creates a strong preference for homeotropic anchoring, wherein the nematic director (molecular orientation) is perpendicular to the drop surface (Fig. 1a). Each surfactant-stabilized NLCO emulsion drop contains a mixture of RM82 monomer and oligomers of RM82 (1,4-bis-[4-(6-Reprints and permissions information is available at www.nature.com/reprints.Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use: