We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona which treats the parameters of turbulence driven by supernovae and by magneto-rotational instability 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 to 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 the large-scale magnetic field , its dependence on the small-scale magnetic helicity fluxes , and the 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 than the field inside the disk and has only a weak impact on the dynamo operation .