Self-assembly is fundamental to the biological function of cells and the fabrication of nanomaterials. However, the origin of the shape of various self-assemblies, such as the shape of cells, is not altogether clear. Polymeric, oligomeric, or low molecular weight amphiphiles are a rich source of nanomaterials, and controlling their self-assembly is the route to tailored nanosystems with specific functionalities. Here, We provide direct evidence that a particular molecular architecture, polymeric branching, leads to a rare form of self-assembly, the planar nanodisc. Cholesterol containing self-assemblies formed from amphiphilic linear or branched cetyl poly(ethylenimine) (Mn similar to 1000 Da) or amphiphilic cetyl poly (propylenimine) dendrimer derivatives (Mn similar to 2000 Da) show that branching, by reducing the hydrophilic headgroup area, alters the shape of the self-assemblies transforming closed 60 nm spherical bilayer vesicles to rare 50 nm x 10 nm planar bilayer discs. Increasing the hydrophilic headgroup area, by the inclusion of methoxy poly(ethylene glycol) moieties into the amphiphilic headgroup, transforms the planar discs to 100 nm spherical bilayer vesicles. This study provides insight into the key role played by molecular shape on molecular self-organization into rare nanodiscs.