Abstract
We discuss the problem of the existence of envelopes of holomorphy of the new cross-type objects, the A -crosses, which leads us to the far-reaching generalizations of the famous Hartogs theorem. We also take under consideration the issue of the existence of ‘nice' general descriptions of envelopes of holomorphy of the cross-like objects in terms of the relative extremal function, which seems to be very natural in the light of the extension theory of separately holomorphic functions on classical crosses and (N, k)-crosses.
