  We consider the standard first passage percolation model on Z^d with a
distribution G on R+ that admits an exponential moment. We study the maximal
flow between a compact convex subset A of R^d and infinity. The study of
maximal flow is associated with the study of sets of edges of minimal capacity
that cut A from infinity. We prove that the rescaled maximal flow between nA
and infinity $\phi$(nA)/n^ (d--1) almost surely converges towards a
deterministic constant depending on A. This constant corresponds to the
capacity of the boundary $\partial$A of A and is the integral of a
deterministic function over $\partial$A. This result was shown in dimension 2
and conjectured for higher dimensions by Garet in [6].
