  We study supersymmetric models with a GUT-sized extra dimension, where both
the Higgs fields and the SUSY breaking hidden sector are localized on a 4D
brane. Exponential wave function profiles of the matter fields give rise to
hierarchical structures in the Yukawa couplings and soft terms. Such structures
can naturally explain hierarchical fermion masses and mixings, while at the
same time alleviating the supersymmetric flavour problem. We discuss two
sources of supersymmetry breaking, radion mediation and brane fields, and
perform a detailed numerical analysis, thoroughly taking into account the
proliferation of unknown O(1) coefficients that occurs in this class of models.
It turns out that additional assumptions on supersymmetry breaking are
necessary to evade the stringent experimental bounds on lepton flavour
violation. The favourable regions of parameter space are then examined with
regards to their LHC phenomenology. They generically feature heavy gluinos and
squarks beyond current bounds. Lepton flavour violation in SUSY cascade decays
can give interesting signatures.
