  We present compact Q-balls in an (Anti-)de Sitter background in D dimensions,
obtained with a V-shaped potential of the scalar field. Beyond critical values
of the cosmological constant compact Q-shells arise. By including the
gravitational back-reaction, we obtain boson stars and boson shells with
(Anti-)de Sitter asymptotics. We analyze the physical properties of these
solutions and determine their domain of existence. In four dimensions we
address some astrophysical aspects.
