Probabilistic flooding has been frequently considered as a suitable dissemination information approach for limiting the large message overhead associated with traditional (full) flooding approaches that are used to disseminate globally information in unstructured peer-to-peer and other networks. A key challenge in using probabilistic flooding is the determination of the forwarding probability so that global network outreach is achieved while keeping the message overhead as low as possible. In this paper, by showing that a probabilistic flooding network, generated by applying probabilistic flooding to a connected random graph network, can be (asymptotically) "bounded" by properly parameterized random graph networks and by invoking random graph theory results, asymptotic values of the forwarding probability are derived guaranteeing (probabilistically) successful coverage, while significantly reducing the message overhead with respect to traditional flooding. Asymptotic express...