In this paper, we study the capacity limits of dense multi antenna systems. We derive asymptotic capacity expressions for point-to-point and broadcast channels by applying recent tools from random matrix theory. In the case of broadcast channels, we focus on linear precoding techniques. We found that the asymptotic capacity depends only on the ratio between the size of the antenna array and the wavelength. This provides useful guidelines on the achievable limits of information transfer. In particular, it is shown that the total capacity grows unbounded if the transmitter has perfect knowledge on the channel, while the capacity saturates in the absence of channel knowledge at the transmitter. We provide numerical results supporting the theoretical derivations.