  We present a model for a global axisymmetric turbulent dynamo operating in a
galaxy with a corona which treats the supernovae (SNe) and magneto-rotational
instability (MRI) driven turbulence parameters under a common formalism. The
nonlinear quenching of the dynamo is alleviated by inclusion of small-scale
advective and diffusive magnetic helicity fluxes, which allow the gauge
invariant magnetic helicity to be transferred outside the disk and consequently
build up a corona during the course of dynamo action. The time-dependent dynamo
equations are expressed in a separable form and solved through an eigenvector
expansion constructed using the steady-state solutions of the dynamo equation.
The parametric evolution of the dynamo solution allows us to estimate the final
structure of the global magnetic field and the saturated value of the
turbulence parameter $\alpha_m$, even before solving the dynamical equations
for evolution of magnetic fields in the disk and the corona, along with
$\alpha$-quenching. We then solve these equations simultaneously to study the
saturation of large-scale magnetic field, its dependence on the small-scale
magnetic helicity fluxes and corresponding evolution of the force-free field in
the corona. The quadrupolar large-scale magnetic field in the disk is found to
reach equipartition strength within a timescale of 1 Gyr. The large-scale
magnetic field in the corona obtained is much weaker in strength compared to
the field inside the disk and has only a weak impact on the dynamo operation.
