  For a subset T of nodes of an undirected graph G, a T-Steiner cut is a cut
\delta(S) where S intersects both T and the complement of T. The T-Steiner cut
dominant} of G is the dominant CUT_+(G,T) of the convex hull of the incidence
vectors of the T-Steiner cuts of G. For T={s,t}, this is the well-understood
s-t-cut dominant. Choosing T as the set of all nodes of G, we obtain the
\emph{cut dominant}, for which an outer description in the space of the
original variables is still not known. We prove that, for each integer \tau,
there is a finite set of inequalities such that for every pair (G,T) with |T|\
<= \tau the non-trivial facet-defining inequalities of CUT_+(G,T) are the
inequalities that can be obtained via iterated applications of two simple
operations, starting from that set. In particular, the absolute values of the
coefficients and of the right-hand-sides in a description of CUT_+(G,T) by
integral inequalities can be bounded from above by a function of |T|. For all
|T| <= 5 we provide descriptions of CUT_+(G,T) by facet defining inequalities,
extending the known descriptions of s-t-cut dominants.
