  With a non local shell model of magnetohydrodynamic turbulence we investigate
numerically the turbulent dynamo action for low and high magnetic Prandtl
numbers ($Pm$). The results obtained in the kinematic regime and along the way
to dynamo saturation are understood in terms of a phenomenological approach
based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy
transfers. In both cases the magnetic energy grows at small scale and saturates
as an inverse `` cascade ''.
