  We study branched covers of curves with specified ramification points, under
a notion of equivalence derived from linear series. In characteristic 0, no
non-constant families of covers with fixed ramification points exist. In
positive characteristic we formulate a necessary and sufficient condition for
the existence of such a family. We unconditionally prove one direction of this
conjecture, and by studying infinitesimal deformations show the other direction
in characteristic 2 and 3.
