The present paper studies the basic physics of the spontaneous fast reconnection model in a three-dimensional (3D) situation for different resistivity parameter values, where the threshold for occurrence of current-driven anomalous resistivity is allowed to increase with the thermal velocity (rootT), and the initial plasma density notably changes in space with the plasma pressure in the current sheet system. For any case, once the anomalous resistivity is ignited, the 3D fast reconnection mechanism explosively evolves as a nonlinear instability by the positive feedback between the anomalous resistivity and the reconnection flow, even if the threshold significantly increases with the thermal velocity; for the larger threshold values, the fast reconnection evolution becomes more drastic and the reconnection rate, finally attained on the nonlinear saturation phase, becomes larger. In the resulting 3D fast reconnection configuration, slow shocks stand and extend outwards in the finite extent; also, ahead of the fast reconnection jet, a large-scale 3D plasmoid swells and propagates in the central current sheet, and a vortex flow is formed near the plasmoid side boundary. In the wide range of parameter values, the basic physics of the 3D spontaneous fast reconnection evolution in the finite extent is found to be, qualitatively, consistent with the well-known two-dimensional one. (C) 2004 American Institute of Physics.