  We study angularly excited as well as interacting non-topological solitons,
so-called Q-balls and their gravitating counterparts, so-called boson stars in
3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge
and arise as solutions of complex scalar field models in a flat space-time
background and coupled minimally to gravity, respectively.
  We present examples of interacting Q-balls that arise due to angular
excitations, which are closely related to the spherical harmonics. We also
construct explicit examples of rotating boson stars that interact with
non-rotating boson stars. We observe that rotating boson stars tend to absorb
the non-rotating ones for increasing, but reasonably small gravitational
coupling. This is a new phenomenon as compared to the flat space-time limit and
is related to the negative contribution of the rotation term to the energy
density of the solutions. In addition, our results indicate that a system of a
rotating and non-rotating boson star can become unstable if the direct
interaction term in the potential is large enough. This instability is related
to the appearance of ergoregions.
