  We study convergence in variation of probability solutions of nonlinear
Fokker-Planck-Kolmogorov equations to stationary solutions. We obtain
sufficient conditions for the exponential convergence of solutions to the
stationary solution in case of coefficients that can have an arbitrary growth
at infinity and depend on the solutions through convolutions with unbounded
discontinuous kernels. In addition, we study a more difficult case where the
nonlinear equation has several stationary solutions and convergence to a
stationary solution depends on initial data. Finally, we obtain sufficient
conditions for solvability of nonlinear Fokker-Planck-Kolmogorov equations.
