  The detailed analytical and numerical analysis of the electron spectrum and
persistent currents and their densities for a Corbino disk in a constant
magnetic field is presented. We calculate the current density profiles and
study their dependence on the inner and outer radius of the Corbino disk. We
study evolution of the persistent currents and track their emergence and decay
for different limiting cases of such a geometry, starting from a nanodot and
ending by a macroscopic circle. The consistency of our results for the currents
is confirmed by the agreement between the direct integration of the
corresponding current densities and the application of the Byers-Yang formula.
The qualitative comparison with the well-known results for quasi-one
dimensional mesoscopic metallic rings is provided. Our study can be applicable
for more accurate treatment and interpretation of the experimental data with
measurements of the persistent currents in different doubly-connected systems.
