  We investigate the dynamo problem in the limit of small magnetic Prandtl
number ($\Pm$) using a shell model of magnetohydrodynamic turbulence. The model
is designed to satisfy conservation laws of total energy, cross helicity and
magnetic helicity in the limit of inviscid fluid and null magnetic diffusivity.
The forcing is chosen to have a constant injection rate of energy and no
injection of kinetic helicity nor cross helicity. We find that the value of the
critical magnetic Reynolds number ($\Rm$) saturates in the limit of small
$\Pm$. Above the dynamo threshold we study the saturated regime versus $\Rm$
and $\Pm$. In the case of equipartition, we find Kolmogorov spectra for both
kinetic and magnetic energy except for wave numbers just below the resistive
scale. Finally the ratio of both dissipation scales (viscous to resistive)
evolves as $\Pm^{-3/4}$ for $\Pm < 1$
