  The classical Brill-Noether theorems count the dimension of the family of
maps from a general curve of genus g to non-degenerate curves of degree d in
r-dimensional projective space. These theorems can be extended to include
ramification conditions at fixed general points. This paper deals with the
problem of imposing a ramification condition at an unspecified point. We solve
the problem completely in dimensions 1 and 2, and provide an existence test and
bound the dimension of the family in the general case.
