  Survival and percolation probabilities are most important quantities in the
theory and in the application of growth models with spreading. We construct
field theoretical expressions for these probabilities which are feasible for
perturbation expansions. The outstanding role of the absorbing noise is
stressed to obtain survival probabilities monotonic decreasing with time. We
briefly consider some fundamental growth models equipped with absorbing noise
which are representations of known universality classes of spreading phenomena.
The critical scaling properties of their survival and percolation and
probabilities are stated. In an appendix we consider shortly the renormalized
field theory of compact directed percolation.
