  The (2 + 1)-dimensional Maxwell-Chern-Simons gauge model consisting of two
complex scalar fields interacting through a common Abelian gauge field is
considered. It is shown that the model has a solution that describes a soliton
system consisting of vortex and Q-ball constituents. This two-dimensional
soliton system possesses a quantized magnetic flux and a quantized electric
charge. Moreover, the soliton system has a nonzero angular momentum. Properties
of this vortex-Q-ball system are investigated by analytical and numerical
methods. It is found that the system combines properties of a vortex and a
Q-ball.
