  We have used a first-principles-based scheme to compute the
temperature-versus-misfit strain ``Pertsev'' phase diagram of ultrathin films
of {\sl incipient} ferroelectric KTaO$_3$. Our results suggest that, at
variance with the bulk material, KTaO$_3$ ultrathin films cannot be described
as quantum paraelectrics. Rather, the behavior of the films is largely
determined by surface/interface effects that favor ferroelectricity and the
imperfect screening of the depolarizing fields. This leads to Pertsev phase
diagrams that are qualitatively similar to those of {\sl normal} ferroelectrics
such as BaTiO$_3$.
