  We consider a general class of three--state models where individuals hold one
of two opposite opinions, or are neutral, and exchange opinions in generic
pairwise interactions. We show that when opinions spread in a population where
a fraction of individuals (zealots) maintain unshakably their opinion, one of
four qualitatively distinct kinds of collective dynamics arise, depending on
the specific rules governing the social interactions. Unsurprisingly, when
their density is high, zealots drive the whole population to consensus on their
opinion. For low densities a rich phase diagram emerges: a finite population of
dissenters can survive and be the only stationary state or may need a critical
mass or dissenters to be sustained; the critical mass may vanish or not as the
density is reduced; the transition to the high density regime can be smooth or
abrupt, and shows interesting hysteretic effects. For each choice of the
interaction rules we calculate the critical density of zealots above which
diverse opinions cannot survive.
