  Pulsar magnetospheres are filled with relativistic pairs copiously emitting
photons detected from the radio wavelengths up to high and very high energies,
in the GeV and sometimes in the TeV range. Efficient particle acceleration
converts the stellar rotational kinetic energy into radio, X-ray and gamma-ray
photons. Force-free magnetospheres, being dissipationless, cannot operate this
conversion. Some non ideal plasma effects must set in within the magnetosphere.
In this paper, we compute numerical solutions of pulsar radiative
magnetospheres in the radiation reaction limit, where radiation fully balances
single particle acceleration. Using an appropriate Ohm's law, the dissipation
is only controlled by the pair multiplicity factor~$\kappa$. Moreover we allow
for either a minimal radiative region where dissipation is added only where
required or for a force-free inside radiative outside model. This approach
naturally and self-consistently connects the particle dynamics to its radiation
field in the ultra-relativistic regime. Our solutions tend to the force-free
limit for moderately large multiplicities, $\kappa \gg 1$, decreasing the
spin-down energy conversion into radiation. Nevertheless, for sufficiently low
multiplicity $\kappa \lesssim1$, a significant fraction of the spin-down energy
flows into radiation via particle acceleration. The work done by the
electromagnetic field on the plasma mainly occurs in the current sheet of the
striped wind, right outside the light-cylinder. Nevertheless the impact on the
magnetic topology is negligible whatever the model. Therefore the associated
sky maps and light-curves are only weakly impacted as shown.
