This paper studies multi-antenna-aided covert communications coexisting with randomly located wardens and interferers, considering both centralized and distributed antenna systems (CAS/DAS). The throughput performance of the covert communication is analyzed and optimized under a stochastic geometry framework, where the joint impact of the small-scale channel fading and the large-scale path loss is examined. To be specific, two probabilistic metrics, namely, the covert outage probability and the connectivity probability, are adopted to characterize the covertness and reliability of the transmission, respectively, and analytically tractable expressions for the two metrics are derived. The worst-case covert communication scenario is then investigated, {where the wardens invariably can maximize the covert outage probability by adjusting the detection thresholds for their detectors}. Afterwards, the optimal transmit power and transmission rate are jointly designed to maximize the covert throughput subject to a covertness constraint. Interestingly, it is found that the maximal covert throughput for both the CAS and DAS is invariant to the density of interferers and the interfering power, regardless of the number of transmit antennas. Numerical results demonstrate that the CAS outperforms the DAS in terms of the covert throughput for the random network of interest, and the throughput gap between the two systems increases dramatically when the number of transmit antennas becomes larger.