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In recently introduced Split Susy theories, in which the scale of Susybreaking is very high, the requirement that the relic abundance of the LightestSuperPartner (LSP) provides the Dark Matter of the Universe leads to theprediction of fermionic superpartners around the weak scale. This is no longerobviously the case if the LSP is a hidden sector field, such as a Gravitino oran other hidden sector fermion, so, it is interesting to study this scenario.We consider the case in which the Next-Lightest SuperPartner (NLSP) freezes outwith its thermal relic abundance, and then it decays to the LSP. We use theconstraints from BBN and CMB, together with the requirement of attaining GaugeCoupling Unification and that the LSP abundance provides the Dark Matter of theUniverse, to infer the allowed superpartner spectrum. As very good news for apossible detaction of Split Susy at LHC, we find that if the Gravitino is theLSP, than the only allowed NLSP has to be very purely photino like. In thiscase, a photino from 700 GeV to 5 TeV is allowed, which is difficult to test atLHC. We also study the case where the LSP is given by a light fermion in thehidden sector which is naturally present in Susy breaking in Extra Dimensions.We find that, in this case, a generic NLSP is allowed to be in the range 1-20TeV, while a Bino NLSP can be as light as tens of GeV.Comment: 29 pages, 12 figures. v2: modified conclusions for bino NLSP. v3:  corrected small mistake in Gauge Coupling Unification, conclusions unchange

How heavy can the fermions in split supersymmetry be? A study on the gravitino and the extradimensional lightest supersymmetric partner