  General hypersurface layers are considered in order to describe brane-worlds
and shell cosmologies. No restriction is placed on the causal character of the
hypersurface which may thus have internal changes of signature. Strengthening
the results in our previous letter [1], we confirm that a good, regular and
consistent description of signature change is achieved in these brane/shells
scenarios, while keeping the hypersurface and the bulk completely regular. Our
formalism allows for a unified description of the traditional timelike
branes/shells together with the signature-changing, or pure null, ones. This
allows for a detailed comparison of the results in both situations. An
application to the case of hypersurface layers in static bulks is presented,
leading to the general Robertson-Walker geometry on the layer --with a possible
signature change. Explicit examples on anti de Sitter bulks are then studied.
The permitted behaviours in different settings ($Z_{2}$-mirror branes,
asymmetric shells, signature-changing branes) are analysed in detail. We show
in particular that (i) in asymmetric shells there is an upper bound for the
energy density, and (ii) that the energy density within the brane vanishes when
approaching a change of signature. The description of a signature change as a
`singularity' seen from within the brane is considered. We also find new
relations between the fundamental constants in the brane/shell, its tension,
and the cosmological and gravitational constants of the bulk, independently of
the existence or not of a change of signature.
