Force-free neutron star magnetospheres are nowadays well known and found through numerical simulations. Even extension to general relativity has recently been achieved. However, those solutions are by definition dissipationless, meaning that the star is unable to accelerate particles and let them radiate any photon. Interestingly, the force-free model has no free parameter however it must be superseded by a dissipative mechanism within the plasma. In this paper, we investigate the magnetosphere electrodynamics for particles moving in the radiation reaction regime, using the limit where acceleration is fully balanced by radiation, also called Aristotelian dynamics. An Ohm's law is derived, from which the dissipation rate is controlled by a one parameter family of solutions depending on the pair multiplicity~$\kappa$. The spatial extension of the dissipation zone is found self-consistently from the simulations. We show that the radiative magnetosphere of an aligned rotator tends to the force-free regime whenever the pair multiplicity becomes moderately large, $\kappa \gg 1$. However, for low multiplicity, a substantial fraction of the spindown energy goes into particle acceleration and radiation in addition to the Poynting flux, the latter remaining only dominant for large multiplicities. We show that the work done on the plasma occurs predominantly in the equatorial current sheet right outside the light-cylinder.