  A family of models of counterrotating and rotating relativistic thin discs of
infinite extension based on a charged and magnetized Kerr-NUT metric are
constructed using the well-known "displace, cut and reflect" method extended to
solutions of vacuum Einstein-Maxwell equations. The metric considered has as
limiting cases a charged and magnetized Taub-NUT solution and the well known
Kerr-Newman solutions. We show that for Kerr-Newman fields the eigenvalues of
the energy-momentum tensor of the disc are for all the values of the parameters
real quantities so that these discs do not present heat flow in any case,
whereas for charged and magnetized Kerr-NUT and Taub-NUT fields we find always
regions with heat flow. We also find a general constraint over the
counterrotating tangential velocities needed to cast the surface
energy-momentum tensor of the disc as the superposition of two counterrotating
charged dust fluids. We show that, in general, it is not possible to take the
two counterrotating fluids as circulating along electrogeodesics nor take the
two counterrotating tangential velocities as equal and opposite.
