  The most general model with a magnetic impurity coupled to hybridizing and
screening channels of a conduction band is considered. The partition function
of the system is asymptotically equivalent to that of the multi-component kink
plasma with a weak external field. The scaling properties of the models for
finite $U$ are sketched by using the Anderson-Yuval-Hamann-Cardy poor man's
scaling theory. We point out that it is proper to include a two-body
hybridization in order to obtain correct renormalization flows. The phase
structures are studied graphically for the general model and various reduced
models. A Fermi-non-Fermi liquid phase transition is found for all the models.
We also show all possible phases with different finite temperature behaviors
though they have the same Fermi liquid fixed point at low temperature. We also
discuss the fixed point behaviors in the mixed valence state regime.
