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We propose a system that transcribes the conversation of a typical meeting scenario that is captured by a set of initially unsynchronized microphone arrays at unknown positions. It consists of subsystems for signal synchronization, including both sampling rate and sampling time offset estimation, diarization based on speaker and microphone array position estimation, multi-channel speech enhancement, and automatic speech recognition. With the estimated diarization information, a spatial mixture model is initialized that is used to estimate beamformer coefficients for source separation. Simulations show that the speech recognition accuracy can be improved by synchronizing and combining multiple distributed microphone arrays compared to a single compact microphone array. Furthermore, the proposed informed initialization of the spatial mixture model delivers a clear performance advantage over random initialization.