  We investigate transport properties of different realizations of
one-dimensional quantum wires coupled to a number of external electrodes in
terms of the full counting statistics. Focusing on the set-ups in which edge
states of Majorana type are realizable we analyze the effects of the exchange
of charge carriers with the environment. We find a very strong suppression of
the non-local current correlations, which decay exponentially with the coupling
strength and the wire length. The local properties such as transport currents
and current correlations measured at individual contacts between the wire and
external electrode turn out to develop asymmetry when energy-resolved. We
provide a number of exact analytical solutions and discuss experimental
implications of our findings.
