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To an equisingularity class of complex plane branches, described by its multiplicity and characteristic exponents , , there is a naturally associated family of equations containing a complete set of analytic representatives for all branches of the class. We show in this paper that the general polar curve of any member of is Newton degenerate, except when , in which case the general member of corresponds to a curve which has a Newton non-degenerate general polar curve with a fixed Newton polygon, or when , , , , with and is odd, in which case has a subset containing a complete set of analytic representatives for all branches of the class whose general member has also a Newton non-degenerate general polar curve with a fixed Newton polygon. In both cases, we give explicit Zariski open sets the points of which represent branches with Newton non-degenerate polars and describe the topology of their general polars. [ABSTRACT FROM AUTHOR]