  The excitation and further sustenance of large-scale magnetic fields in
rotating astrophysical systems, including planets, stars and galaxies, is
generally thought to involve a fluid magnetic dynamo effect driven by helical
magnetohydrodynamic turbulence. While this scenario is appealing on general
grounds, it however currently remains largely unconstrained, notably because a
fundamental understanding of the nonlinear asymptotic behaviour of large-scale
fluid magnetism in the astrophysically-relevant but treacherous regime of large
magnetic Reynolds number $Rm$ is still lacking. We explore this problem using
local high-resolution simulations of turbulent magnetohydrodynamics driven by
an inhomogeneous helical forcing generating a sinusoidal profile of kinetic
helicity, mimicking the hemispheric distribution of kinetic helicity in
rotating turbulent fluid bodies. We identify a transition at large $Rm$ to a
nonlinear state, followed up to $Rm\simeq 3\times 10^3$, consisting of strong,
saturated small-scale magnetohydrodynamic turbulence and a weaker, travelling
coherent large-scale field oscillation. This state is characterized by an
asymptotically small resistive dissipation of magnetic helicity, by its spatial
redistribution across the equator through turbulent fluxes driven by the
hemispheric distribution of kinetic helicity, and by the tentative presence in
the tangled dynamical magnetic field of plasmoids typical of reconnection at
large $Rm$.
