  A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2
orbifolds is considered and the free theory of 6D chiral fermions studied on
it. As the orbifold limit is taken, localized 4D chiral massless fermions are
seen to arise at the fixed points. Their number, location and chirality is
found to be independent on the detailed profile of the resolving space and to
agree with the result of hep-th/0409229, in which a particular resolution was
employed. As a consistency check of the resolution procedure, the massive
equation is numerically studied. In particular, for S^1/Z_2, the "resolved"
mass--spectrum and wave functions in the internal space are seen to correctly
reproduce the usual orbifold ones, as the orbifold limit is taken.
