  An open problem in polarization theory is to determine the binary operations
that always lead to polarization (in the general multilevel sense) when they
are used in Ar{\i}kan style constructions. This paper, which is presented in
two parts, solves this problem by providing a necessary and sufficient
condition for a binary operation to be polarizing. This (second) part provides
a foundation of polarization theory based on the ergodic theory of binary
operations which we developed in the first part. We show that a binary
operation is polarizing if and only if it is uniformity preserving and its
right-inverse is strongly ergodic. The rate of polarization of single user
channels is studied. It is shown that the exponent of any polarizing operation
cannot exceed $\frac{1}{2}$, which is the exponent of quasigroup operations. We
also study the polarization of multiple access channels (MAC). In particular,
we show that a sequence of binary operations is MAC-polarizing if and only if
each binary operation in the sequence is polarizing. It is shown that the
exponent of any MAC-polarizing sequence cannot exceed $\frac{1}{2}$, which is
the exponent of sequences of quasigroup operations.
