  We study two different types of systems with many absorbing states (with and
without a conservation law) and scrutinize the effect of walls/boundaries
(either absorbing or reflecting) into them. In some cases, non-trivial
structured absorbing configurations (characterized by a background field)
develop around the wall. We study such structures using a mean-field approach
as well as computer simulations. The main results are: i) for systems in the
directed percolation class, a very fast (exponential) convergence of the
background to its bulk value is observed; ii) for systems with a conservation
law, power-law decaying landscapes are induced by both types of walls: while
for absorbing walls this effect is already present in the mean-field
approximation, for reflecting walls the structured background is a
noise-induced effect. The landscapes are shown to converge to their asymptotic
bulk values with an exponent equal to the inverse of the bulk correlation
length exponent. Finally, the implications of these results in the context of
self-organizing systems are discussed.
