We construct a novel scattering theory to investigate magnetoelectrically inducedspin polarizations. Local spin polarizations generated by electric currents passingthrough a spin–orbit-coupled mesoscopic system are measured by an external probe.The electrochemical and spin-dependent chemical potentials on the probe arecontrollable and tuned to values ensuring that neither charge nor spin current flowbetween the system and the probe, on time average. For the relevant case of asingle-channel probe, we find that the resulting potentials are exactly independent of thetransparency of the contact between the probe and the system. Assuming thatspin relaxation processes are absent in the probe, we therefore identify the localspin-dependent potentials in the sample at the probe position, and hence thelocal current-induced spin polarization, with the spin-dependent potentials in theprobe itself. The statistics of these local chemical potentials is calculated withinrandom matrix theory. While they vanish on spatial and mesoscopic average,they exhibit large fluctuations, and we show that single systems typically havespin polarizations exceeding all known current-induced spin polarizations by aparametrically large factor. Our theory allows us to calculate quantum correlationsbetween spin polarizations inside the sample and spin currents flowing out of it. Weshow that these large polarizations correlate only weakly with spin currents inexternal leads, and that only a fraction of them can be converted into a spincurrent in the linear regime of transport, which is consistent with the mesoscopicuniversality of spin conductance fluctuations. We numerically confirm the theory.