A critical analysis of standard accretion models is presented. We cons
ider the stability of models in the theories of disc accretion onto bl
ack holes and spherical/disc accretion onto a magnetosphere. We take i
nto account realistic physics processes and geometry (inner magnetic f
ield in the accreted plasma, finite conductivity, finite length of the
field lines, finite rotation of the accreted object, and magnetic she
ar on the boundary between the magnetosphere and accreted plasma). The
influence of these factors leads to radical changes of both the accre
tion as whole and the energy release in the accreting system. Strong c
urrent-sheet and Z-pinch-like structures should arise over the polar r
egion of the accreting object. Particle acceleration in the electric f
ields of current discharges in these regions may be a source of effici
ent conversion of energy into nonthermal particles and of the emission
observed from many accreting objects.