The sphere to cylinder transition in a one-phase droplet microemulsion system is studied theoretically. Within the framework of the curvature energy model by Helfrich, it was already shown by Safran [J. Phys. (France) Lett. 45, L-69 (1984)] that for a certain range of the curvature parameters (rigidity constants and spontaneous curvature), a transition occurs from spherical droplets to infinitely long cylinders through a region where both spheres and cylinders are present. Our aim is to further investigate this region in a quantitative way by including-in addition to curvature energy-translation entropy, cylinder length polydispersity, and radial polydispersity. In this way we are able to obtain structural information on the spheres and cylinders formed, their respective volume fractions, and polydispersity, and provide a more detailed comparison with experimental results.