  A theorem due to Kazhdan and Ziegler implies that, by substituting linear
forms for its variables, a homogeneous polynomial of sufficiently high strength
specialises to any given polynomial of the same degree in a bounded number of
variables. Using entirely different techniques, we extend this theorem to
arbitrary polynomial functors. As a corollary of our work, we show that
specialisation induces a quasi-order on elements in polynomial functors, and
that among the elements with a dense orbit there are unique smallest and
largest equivalence classes in this quasi-order.
