This paper provides an analytical performance characterization of user-centric cooperation for network multiple-input multiple-output (MIMO) systems, where base-stations (BSs) form finite-sized clusters to jointly transmit information to and receive information from multiple mobile users. In the user-centric model, the cooperation BS cluster for each user is formed individually and may overlap with each other. The size of cluster determines the amount of backhaul and channel state information needed for implementation. The BSs are equipped with multiple antennas; multiple single-antenna users are served simultaneously; the cooperating BSs perform zero-forcing beamforming across the cluster. By using a stochastic geometry model where the BSs and the users form Poisson point processes over the two-dimensional plane and by further approximating both the signal and interference powers using Gamma distributions of appropriate parameters, this paper shows that regardless of clustering strategy, network MIMO provides sum-rate gain for both uplink (UL) and downlink (DL) transmission as compared to single-cell processing. The gain is about 30%-60% at cluster size of 10 for typical deployment; it is larger in DL than UL in a typical deployment due to the larger DL transmit power. More significantly, network MIMO can provide 300% gain or more for cluster-edge users, but only for the DL and only with user-centric clustering. This highlights the conclusion that performance evaluation for network MIMO should focus on DL cluster-edge users and on the user-centric clustering strategy.