  In numerical studies of turbulence, hyperviscosity is often used as a tool to
extend the inertial subrange and to reduce the dissipative subrange. By
analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in
magnetohydrodynamics. The underlying assumption is that only the small scales
are affected by this manipulation. In the present paper, possible side effects
on the evolution of the large scale magnetic field are investigated. It is
found that for turbulent flows with helicity, hyperdiffusivity causes the
dynamo-generated magnetic field to saturate at a higher level than normal
diffusivity. This result is successfully interpreted in terms of magnetic
helicity conservation, which also predicts that full saturation is only reached
after a time comparable to the large scale magnetic (hyper)diffusion time.
