  We model the transmission of information of a message on the Erd\"os-R\'eny
random graph with parameters $(n,p)$ and limited resources. The vertices of the
graph represent servers that may broadcast a message at random. Each server has
a random emission capital that decreases by one at each emission. We examine
two natural dynamics: in the first dynamics, an informed server performs its
attempts, then checks at each of them if the corresponding edge is open or not;
in the second dynamics the informed server knows a priori who are its
neighbors, and it performs all its attempts on its actual neighbors in the
graph. In each case, we obtain first and second order asymptotics (law of large
numbers and central limit theorem), when $n\to \infty$ and $p$ is fixed, for
the final proportion of informed servers.
