  Multipartite entanglement has been shown to be of particular relevance for a
better understanding and exploitation of the dynamics and flow of entanglement
in multiparty systems. This calls for analysis aimed at identifying the
appropriate processes that guarantee the emergence of multipartite entanglement
in a wide range of scenarios. Here we carry on such analysis considering a
system of two initially entangled qubits, one of which is let to interact with
a third qubit according to an arbitrary unitary evolution. We establish
necessary and sufficient conditions on the corresponding Kraus operators, to
discern whether the evolved state pertains to either one of the classes of
3-qubit pure states that exhibit some kind of entanglement, namely biseparable,
W-, and GHZ- genuine entangled classes. Our results provide a classification of
the Kraus operators according to their capacity of producing 3-qubit
entanglement, and pave the way for extending the analysis to larger systems and
determining the particular interactions that must be implemented in order to
create, enhance and distribute entanglement in a specific manner.
