  We have in detail characterized the anisotropic charge response of the dimer
Mott insulator $\kappa$-(BEDT-TTF)$_2$\-Cu$_2$(CN)$_3$ by dc conductivity, Hall
effect and dielectric spectroscopy. At room temperature the Hall coefficient is
positive and close to the value expected from stoichiometry; the temperature
behavior follows the dc resistivity $\rho(T)$. Within the planes the dc
conductivity is well described by variable-range hopping in two dimensions;
this model, however, fails for the out-of-plane direction. An unusually broad
in-plane dielectric relaxation is detected below about 60 K; it slows down much
faster than the dc conductivity following an Arrhenius law. At around 17 K we
can identify a pronounced dielectric anomaly concomitantly with anomalous
features in the mean relaxation time and spectral broadening. The out-of-plane
relaxation, on the other hand, shows a much weaker dielectric anomaly; it
closely follows the temperature behavior of the respective dc resistivity. At
lower temperatures, the dielectric constant becomes smaller both within and
perpendicular to the planes; also the relaxation levels off. The observed
behavior bears features of relaxor-like ferroelectricity. Because
heterogeneities impede its long-range development, only a weak tunneling-like
dynamics persists at low temperatures. We suggest that the random potential and
domain structure gradually emerge due to the coupling to the anion network.
