Infra-red fixed point structure of soft supersymmetry breaking mass terms

We show that the soft SUSY breaking mass terms may have infra-red stable fixed points at which they are related to the gaugino masses and argue that in a generic unification these masses should lie close to their fixed points. We consider the implications for the family dependence of squark and slepton masses and the related flavour changing neutral currents and determine conditions under which models with flavour changing couplings and masses at a high scale may lead to a family independent effective theory at low scales. The analysis is illustrated for a variety of models for which we compute both the fixed point structure and determine the rate of approach to the fixed point.