  Equations of motion for a real self-gravitating scalar field in the
background of a black hole with negative cosmological constant were solved
numerically. We obtain a sequence of static axisymmetric solutions representing
thick domain wall cosmological black hole systems, depending on the mass of
black hole, cosmological parameter and the parameter binding black hole mass
with the width of the domain wall. For the case of extremal cosmological black
hole the expulsion of scalar field from the black hole strongly depends on it.
