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In this work, we consider the multiple antenna systems in which a large number of antennas occupy a given physical volume, and investigate the behavior of the capacity when increasing the number of antennas. In this regime the assumptions of the standard multiple antenna models become questionable. We introduce several new channel models that better fit this scenario and show that for such "spatially dense" multiple antenna systems, one should expect the behavior of the capacity to be qualitatively different than what the standard of multiple antenna models predict.