  A leading candidate for experimental confirmation of the non-local quantum
dynamics of Majorana fermions is the topological Kondo effect, predicted for
mesoscopic superconducting islands connected to metallic leads. We identify an
anisotropic, Toulouse-like, limit of the topological Kondo problem where the
full nonequilibrium conductance and shot noise can be calculated exactly. Near
the Kondo fixed point, we find novel asymptotic features including a universal
conductance scaling function, and fractional charge quantisation observable via
the Fano factor. In the universal regime, our results apply for generic
anisotropy and even away from the Kondo limit as long as the system supports an
emergent topological Kondo fixed point. Our approach thus provides key new
qualitative insights and exact expressions for quantitative comparisons to
future experimental data.
