We present kinematic mean-field dynamo models for galaxies consisting of a turbulent gas disc embedded in a low-conductivity spherical halo. In the cases investigated an axisymmetric mode is the dominant one. This mode can be of either even or odd parity (S0 or A0, respectively). The preference of S0 or A0 modes is governed mainly by the radial profiles of the alpha effect and the turbulent magnetic diffusivity. If the gas disc extends into the galactic centre, the dominant mode is of A0 type and it is concentrated within the central region. If the model is changed so that induction effects are absent in the centre, the dominant mode is an axisymmetric spiral of even parity. We point out that a finite disc thickness and a low-conductivity halo will both lead to appreciable vertical magnetic fields outside the disc plane, and this may affect the interpretation of polarisation observations. We integrate the transfer equations for the three Stokes parameters I, Q, and U and produce in this way synthetic maps for the observed polarisation and rotation measures. Assuming a disc-like distribution of relativistic electrons, our models suggest that for moderate disc thickness modifications of the observed polarised emission due to fields above the plane are minor. For more extended electron distributions quite complicated polarisation patterns are obtained. Still, qualitatively the criteria distinguishing axisymmetric and bisymmetric spiral patterns remain valid.