The Jackiw-Pi model of the self-gravitating gas of nonrelativistic bosons coupled to the Chern-Simons gauge field is known to exhibit asymptotically vanishing, lump-like soliton solutions. Here we discuss a recently proposed generalisation of this theory, which is applicable to systems of repulsive particles and allows to incorporate asymptotically nonvanishing fields, in particular topological vortices. We demonstrate the absence of the condensate state in the Jackiw-Pi model, relate this fact to a particular Lagrangian formulation of its nongauged precursor and derive the new model by modifying this Lagrangian appropriately and using it as a basis for the gauge theory. Reformulating the modified model as a constrained Hamiltonian system allows us to find the self-duality limit in the pure Chern-Simons and in the mixed Chern-Simons-Maxwell cases. These self-duality equations are shown to exhibit both asymptotically nonvanishing topological vortices and lump solitons.