This paper investigates the problem of deploying a network of passive sensors to estimate the positions of an unknown number of stationary transient emitters. Since a completely connected net-work, which has a link between every pair of nodes, is not feasible because of the power and bandwidth constraints, we developed a distributed algorithm that relies only on local communications between neighboring sensors. This distributed algorithm requires information diffusion within the network with the goal that every node achieves all target location estimates as accurate as a fusion center with centralized access to all information. The locations of the emitters are not completely observable by any single sensor since bearings and times of arrival with origin uncertainty are the only available measurements. These measurements are modeled as a realization of a Poisson point process at each sensor. The problem is formulated as a constrained optimization problem, which is solved via an alternating direction method of multipliers in a distributed manner based on the expectation maximization and averaging consensus algorithms. Consensus on the number of candidate targets as well as the inter-node estimate association are addressed so that the distributed algorithm converges to the maximum likelihood estimate. A likelihood function based approach using the estimated probability of detection is presented to determine the number of targets. Simulation results show that the distributed algorithm converges very fast and the root mean square error of target locations is almost as small as that obtained using the centralized algorithm. It is also shown that one can accurately determine the number of targets using the estimated probability of detection.