This paper advocates an application of the fractal topology formalism to an analysis of the magnetotail current systems. Our main attention is concentrated on the magnetotail regions with the considerably stretched background magnetic field; such conditions can be the case in the distant tail, as well as in the near-Earth tail at the late substorm growth phase. Structural properties of the current system at the self-organized (quasi)stationary states are analyzed in relationship with the universal fractal geometry of the percolating fractal sets near the critical threshold. We found that the violation of the criticality character leads to the topological phase transition in the system; this transition has features of a structural catastrophe and is associated with the magnetospheric substorm onset. A comparison with various observational studies is given, and the possible directions of the future research are outlined. ¿ 2001 American Geophysical Union