Distributed co-ordination is the result of dynamical processes enabling independent agents to coordinate their actions without the need of a central co-ordinator. In the past few years, several computational models have illustrated the role played by such dynamics for self-organizing communication systems. In particular, it has been shown that agents could bootstrap shared convention systems based on simple local adaptation rules. Such models have played a pivotal role for our understanding of emergent language processes. However, only few formal or theoretical results have been published about such systems. Deliberately simple computational models are discussed in this paper in order to make progress in understanding the underlying dynamics responsible for distributed coordination and the scaling laws of such systems. In particular, the paper focuses on explaining the convergence speed of those models, a largely under-investigated issue. Conjectures obtained through empirical and qualitative studies of these simple models are compared with results of more complex simulations and discussed in relation to theoretical models formalized using Markov chains, game theory and Polya processes.