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This paper presents a solution for the autonomous exploration and inspection of Ballast Water Tanks (BWTs) of marine vessels using aerial robots. Ballast tank compartments are critical for a vessel's safety and correspond to confined environments often connected through particularly narrow manholes. The method enables their volumetric exploration combined with visual inspection subject to constraints regarding the viewing distance from a surface. We present evaluation studies in simulation, in a mission consisting of 18 BWT compartments, and in 3 field experiments inside real vessels. The data from one of the experiments is also post-processed to generate semantically-segmented meshes of inspection-important geometries. Geometric models can be associated with onboard camera images for detailed and intuitive analysis.