Angular momentum is transported outwards through an accretion disc by magnetohydrodynamical (MHD) turbulence thus allowing material to accrete on to the central object. The magnetorotational instability (MRI) requires a minimum ionization fraction to drive turbulence in a disc. The inner parts of the disc around a young stellar object are sufficiently hot to be thermally ionized. Further out, cosmic rays ionize the surface layers and a dead zone forms at the mid-plane where the disc is too cool for the MRI to operate. The surface density in the turbulent active layer is often assumed to be constant with radius because the cosmic rays penetrate a constant layer. However, if a critical magnetic Reynolds number, ReM, crit, is used to determine the extent of the dead zone, the surface density in the layer generally increases with radius. For small critical magnetic Reynolds number of the order of 1, the constant-layer approximation may be a reasonable fit. However, MHD simulations suggest that the critical magnetic Reynolds number may be much larger, of the order of 104. Analytical fits for the surface density in the magnetic active layer show that , at temperature T and radius R, are a good fit for higher critical magnetic Reynolds number. For the metallicity variation between our Galaxy, the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), there should be no significant difference in the extent of the dead zone. Observations suggest an increase in the lifetime of the disc with decreasing metallicity, which cannot be explained by the dead-zone structure (ignoring possible differences in dust abundances).