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In a broadcasting task, source node wants to send the same message to all the other nodes in the network. Existing solutions address specific mobility scenarios, e.g. connected dominating set (CDS) based for static networks, blind flooding for moderate mobility, hyper flooding for highly mobile and frequently partitioned networks. We are interested in designing a unique protocol that will seamlessly (without using any parameter) adjust itself to any mobility scenario, and with capability to address various model assumptions and optimality criteria. Existing approaches for all scenarios are based on some threshold parameters (e.g. speed) to locally select among different algorithms, and therefore different nodes may run different algorithms. Here we describe a novel general BSM (Broadcasting from Static to Mobile) framework, built over several recent algorithms handling special cases. It aims at high delivery rate with low message cost, and addresses intermittent connectivity and delay minimization. Each node activates with respect to broadcast message whenever it identifies one or more neighbors in need of the message. It selects, upon activation, waiting time (dynamically adjusted with reception of any message) depending on the number of such neighbors, distance to their centroid, and its CDS membership. It competes (at MAC layer) to retransmit at timeout expiry if it still believes that a neighbor needs message. We map this algorithm to variety of multi-hop wireless networks scenarios, with and without: positional information, acknowledgments, and time criticality goal. Some existing solutions are derived as special cases, and we also show how to timely deliver warnings in vehicular networks with arbitrary road structure, without using road maps.