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Heterogeneous base stations (e.g., picocells, microcells, femtocells, and distributed antennas) will become increasingly essential for cellular network capacity and coverage. Up until now, little basic research has been done on the fundamentals of managing so much infrastructure-much of it unplanned-together with the carefully planned macro-cellular network. Inter-cell coordination is in principle an effective way of ensuring different infrastructure components behave in a way that increases, rather than decreases, the key quality of service (QoS) metrics. The success of such coordination depends heavily on how the overhead is shared, and the rate and delay of the overhead sharing. We develop a novel framework to quantify overhead signaling for inter-cell coordination, which is usually ignored in traditional 1-tier networks, and assumes even more importance in multi-tier heterogeneous cellular networks (HCNs). We derive the overhead quality contour for general -tier HCNs-the achievable set of overhead packet rate, size, delay, and outage probability-in closed-form expressions or computable integrals under general assumptions on overhead arrivals and different overhead signaling methods (backhaul and/or wireless). The overhead quality contour is further simplified for two widely used models of overhead arrivals: Poisson and deterministic arrival process. This framework can be used in the design and evaluation of any inter-cell coordination scheme. It also provides design insights on backhaul and wireless overhead channels to handle specific overhead signaling requirements.