  We demonstrate the full power of nonperturbative renormalisation group
methods for nonequilibrium situations by calculating the quantitative phase
diagrams of simple branching and annihilating random walks and checking these
results against careful numerical simulations. Specifically, we show, for the
2A->0, A -> 2A case, that an absorbing phase transition exists in dimensions
d=1 to 6, and argue that mean field theory is restored not in d=3, as suggested
by previous analyses, but only in the limit d -> $\infty$.
