  We study analytically the general features of electroweak symmetry breaking
in the context of the Minimal Supersymmetric Standard Model extended by one
Higgs singlet. The exact analytical forms of the renormalization group
evolutions of the Yukawa couplings and of the soft supersymmetry breaking
parameters are derived to one-loop order. They allow on one hand controllable
approximations in closed analytical form, and on the other a precise study of
the behaviour of infrared quasi fixed point regimes which we carry out. Some of
these regimes are shown to be phenomenologically inconsistent, leading to too
small an effective $\mu$-parameter. The remaining ones serve as a suitable
benchmark to understand analytically some salient aspects, often noticed
numerically in the literature, in relation to the electroweak symmetry breaking
in this model. The study does not need any specific assumption on $\tan \beta$
or on boundary conditions for the soft supersymmetry breaking parameters, thus
allowing a general insight into the sensitivity of the low energy physics to
high energy assumptions.
