  One can easily show that any meromorphic function on a complex closed Riemann
surface can be represented as a composition of a birational map of this surface
to CP^2 and a projection of the image curve from an appropriate point p in CP^2
to the pencil of lines through p. We introduce a natural stratification of
Hurwitz spaces according to the minimal degree of a plane curve such that a
given meromorphic function can be represented in the above way and calculate
the dimensions of these strata.
