We establish the existence and uniqueness of radially symmetric self-d
ual topological vortices in the p = 2 members of the hierarchies of (g
eneralised) Chern-Simons Higgs and Abelian Higgs models. We also obtai
n all possible symmetric nontopological vortices in the Chern-Simons m
odel characterised by an additional parameter governing the decay rate
s of the fields.