  We carry out a comprehensive analysis of the nonminimal supersymmetric
standard model (NMSSM) with baryon and lepton number violation. We catalogue
the baryon and lepton number violating dimension four and five operators of the
model. We then study the renormalization group evolution and infrared stable
fixed points of the Yukawa couplings and the soft supersymmetry breaking
trilinear couplings of this model with baryon and lepton number (and R-parity)
violation involving the heaviest generations. We show analytically that in the
Yukawa sector of the NMSSM there is only one infrared stable fixed point. This
corresponds to a non-trivial fixed point for the top-, bottom-quark Yukawa
couplings and the $B$ violating coupling $\lambda_{233}''$, and a trivial one
for all other couplings. All other possible fixed points are either unphysical
or unstable in the infrared region. We also carry out an analysis of the
renormalization group equations for the soft supersymmetry breaking trilinear
couplings, and determine the corresponding fixed points for these couplings. We
then study the quasi-fixed point behaviour, both of the third generation Yukawa
couplings and the baryon number violating coupling, and those of the soft
supersymmetry breaking trilinear couplings. From the analysis of the fixed
point behaviour, we obtain upper and lower bounds on the baryon number
violating coupling $\lambda_{233}''$, as well as on the soft supersymmetry
breaking trilinear couplings. Our analysis shows that the infrared fixed point
behavior of NMSSM with baryon and lepton number violation is similar to that of
MSSM.
