  We consider scenarios where Dark Matter (DM) particles carry baryon and/or
lepton numbers, which can be defined if there exist operators connecting the
dark to the visible sector. As a result, the DM fields become intimately linked
to the Standard Model (SM) ones and can be maximally asymmetric just like the
ordinary matter. In particular, we discuss minimal scenarios where the DM is a
complex scalar or a Dirac fermion coupled to operators with nonzero baryon
and/or lepton numbers, and that consist of only SM fields. We consider an
initial asymmetry stored in either the SM or the DM sector; the main role of
these operators is to properly $share$ the asymmetry between the two sectors,
in accordance with observations. After the chemical decoupling, the DM and SM
sectors do $not$ $care$ about each other as there is only an ineffective
communication between them. Once the DM mass is specified, the Wilson
coefficients of these operators are fixed by the requirement of the correct
transfer of the asymmetry. We study the phenomenology of this framework at
colliders, direct detection and indirect detection experiments. In particular,
the LHC phenomenology is very rich and can be tested in different channels such
as the two same-sign leptons with two jets, monojet and monojet with a
monolepton.
