We investigate the fluid structure and self-assembly of a system of Janus dumbbells by means of aggregation-volume-bias Monte Carlo simulations and Simulated Annealing techniques. In our approach, Janus dumbbells model asymmetric colloidal particles constituted by two tangent (touching) spheres (labelled as h and s) of different sizes and interaction properties: specifically, the h spheres interact with all other spheres belonging to different dumbbells via hard-sphere potentials, whereas two s spheres interact via a square-well potential. By introducing a parameter α ∈ [0,2] that controls the size ratio between the h and s spheres, we are able to investigate the overall phase behaviour of Janus dumbbells as a function of α. In a previous paper (O'Toole et al., Soft Matter, 2017, 13, 803) we focused on the region where the s sphere is larger than the h sphere (α > 1), documenting the presence of a variety of phase behaviours. Here we investigate a different regime of size ratios, predominantly where the hard sphere is larger than (or comparable to) the attractive one. Under these conditions, we observe the onset of many different self-assembled super-structures. Depending on the specific value of α we document the presence of spherical clusters (micelles) progressively evolving into more exotic structures including platelets, filaments, networks and percolating fluids, sponge structures and lamellar phases. We find no evidence of a gas-liquid phase separation for α ≤ 1.1, since under these conditions it is pre-empted by the development of self-assembled phases.