In this paper, we investigate the asymptotic mutual information expression and the capacity-achieving input covariance matrices for the coordinated multi-point multiple-input multiple-output (MIMO) antenna channels. In particular, it is considered that the numbers of antennas at the transmitter and receiver approach to infinity with a fixed ratio. Our derivations are based on novel techniques from large dimensional random matrix theory. In contrast to previous studies, we consider a general model in which the correlation matrices are generally nonnegative definite and the channel entries are non-Gaussian distributed. We show that the asymptotic capacity is invariant to all types of fading distribution. As such, the asymptotic mutual information expression is robust and has wide applicability.