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Flooding is well known to be the ldquofastestrdquo way to propagate information throughout a network (achieve 100% coverage), at the expense of typically unacceptably large message-forwarding overhead; when the overhead is controlled or limited, then the achieved coverage is reduced. A Single Random Walker (SRW) is another popular mechanism for information dissemination that is very ldquoslowrdquo compared to flooding but utilizes less overhead and can potentially achieve better coverage than flooding. The latter may be attributed to the better ldquostretchingrdquo properties (ability to visit further away network regions) of the SRW and is particularly observed if coverage is defined as the set of network nodes which are at most L hops away from a network node which received the information (notion of L-coverage, L ges 0). Randomly Replicated Random Walkers (RRRWs) are considered in this paper as a broad class of information dissemination mechanisms whose members are defined by a given value of the (first) replication probability; clearly a SWR corresponds to the RRRWs with zero (first) replication probability, while for values of the (first) replication probability close to one a large number of information disseminating agents (RWs) are generated resembling the operation of flooding. By considering various performance metrics (such as the achieved coverage for a given message-forwarding budget and the time required to spend the available message-forwarding budget), and by considering various network topologies (such as Random Geometric, Erdos-Renyi and Clustered environments), we show that the class of RRRWs can ldquofillrdquo the performance space, between the performance induced by flooding and the SRW, thus offering a richer set of information dissemination strategies that can better match desirable performance constraints or objectives.