  All spaces (and groups) are assumed to be separable and metrizable. Jan van
Mill showed that every analytic group $G$ is Effros (that is, every continuous
transitive action of $G$ on a non-meager space is micro-transitive). We
complete the picture by obtaining the following results: under $\mathsf{AC}$,
there exists a non-Effros group; under $\mathsf{AD}$, every group is Effros;
under $\mathsf{V=L}$, there exists a coanalytic non-Effros group. The above
counterexamples will be graphs of discontinuous homomorphisms.
