Processes observed in experiments with the initiation and propagation of divergent detonation in a narrow gap between plates was simulated. The detonation wave is formed in a round tube adjoined to one of the plates at a right angle. Complicated cellular structures of the 2D detonation have been obtained. The process of formation of 3D cellular detonation in channels of square, rectangular, circular, and elliptical cross sections was studied. The process of spontaneous formation of spin detonation in channels of circular cross section was considered. Calculations of the transition of spin detonation to the channel of larger or smaller diameter were conducted and conditions of self-sustained spin detonation were formulated. Detonation is initiated in a quiescent combustible mixture by an instantaneous homogeneous electric discharge in a finite-width zone near the flat closed end of the channel. All computations of 3D detonation were performed in a correct formulation for the entire channel of large length (1 m) rather than only in a certain zone moving together with the wave.