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The hospital system is a complex service system in which patients and hospitals interact and make their decisions based on bounded rationality and information. In this paper, we develop a generative agent-based model to simulate the behavior of a hospital service system. Our model combines agent-based simulation and queueing models to mimic the hospital service processes. Our goal is to simulate and understand the growth and size distribution of hospitals. This simulation model includes agents for supply elements (i.e., hospitals with different resources and expansion strategies) and demand elements (i.e., patients with different preferences for their hospital selections) in a hospital service system. Three important questions are investigated: 1) what is the emergent size distribution of hospitals? 2) what key factors influence the size distribution? and 3) how sensitive is the size distribution to these key factors? Simulation results show that the size distribution is neither power law nor lognormal. Rather, the distribution is leptokurtic, and more skewed than normal but less skewed than lognormal. This result contradicts those in extant literature on the size distributions of human and natural systems, including cities, firms, power-grids, and citation network. We conduct a set of experiments to identify the generative mechanisms for the hospital size distribution and to test the robustness of the results. The model was validated empirically by using a U.S. hospital size dataset. [ABSTRACT FROM AUTHOR]