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Partial base station coordination is analyzed on the downlink of a cellular system with randomly deployed base stations. In contrast with existing work, a stochastic geometry framework is considered for both base station deployment and base station clustering. The cluster-cells form a Poisson tessellation of the plane generated by Poisson distributed cluster base stations. Inter-cell interference nulling is applied to coordinate interference inside each cluster-cell. Both perfect and limited channel state information (CSI) sharing among coordinating base stations are considered. The average achievable rate with perfect CSI and the mean loss in rate due to limited CSI feedback are derived for a typical user inside the cell. Numerical results show that the average achievable rate with interference coordination as well as the mean loss in rate with equal-bit partitioning increase with increasing average cluster size and increasing number of antennas at the transmitter.