Stationary distribution of finite-size systems with absorbing states

We introduce a procedure that allows us to obtain nontrivial stationary distributions of finite-size models with absorbing states. Two models are studied: the contact process and the sandpile model with height restriction. To avoid the permanence of the system in the absorbing state we create a small perturbation that drives the system out of the absorbing state. In the former model a particle is created, in the latter an active site is created. The stationary distributions around the critical point are analyzed by the use of finite-size scaling.