  When magnetic energy density is much larger than that of matter, as in
pulsar/black hole magnetospheres, the medium becomes force-free and we need
relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD),
Alfv\'enic MHD turbulence in the relativistic limit can be described by
interactions of counter-traveling wave packets. In this paper we numerically
study strong imbalanced MHD turbulence in such environments. Here, imbalanced
turbulence means the waves traveling in one direction (dominant waves) have
higher amplitudes than the opposite-traveling waves (sub-dominant waves). We
find that (1) spectrum of the dominant waves is steeper than that of
sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than
that of sub-dominant waves, and (3) the dependence of the ratio of magnetic
energy densities of dominant and sub-dominant waves on the ratio of energy
injection rates is steeper than quadratic (i.e., \$b_+^2/b_-^2 \propto
(\epsilon_+/\epsilon_-)^n \$ with n>2). These results are consistent with those
obtained for imbalanced non-relativistic Alfv\'enic turbulence. This
corresponds well to the earlier reported similarity of the relativistic and
non-relativistic balanced magnetic turbulence.
