We propose a distributed deployment solution for a group of networked agents that should provide a service for a large set of targets, which densely populate a finite area. The agents are heterogeneous in the sense that their quality of service (QoS), modeled as spatial Gaussian distribution, is different. To provide the best service, the objective is to deploy the agents such that their collective QoS distribution is as close as possible to the density distribution of the targets in the sense of the Kullback-Leibler divergence (KLD) measure. We propose a distributed consensus-based expectation-maximization (EM) algorithm to estimate the target density distribution, modeled as a Gaussian mixture model (GMM). Different than the existing algorithms, our proposed distributed EM algorithm enables every agent in the network to obtain an estimate of the GMM model of the distribution of the targets even if only a subset of agents can measure the targets locally. The GMM not only gives an estimate of the targets’ distribution but also clusters the targets to a set of subgroups, each of which is represented by one of the GMM’s Gaussian bases. We use the KLD measure to evaluate the similarity between the QoS distribution of each agent and each Gaussian basis/cluster. A distributed assignment problem is then formulated and solved as a discrete optimal mass transport problem that allocates each agent to a target cluster by taking the KLD as the assignment cost. We demonstrate our results by a sensor deployment for event detection where the sensor’s QoS is modeled as an anisotropic Gaussian distribution.