  We devise a deterministic algorithm for minimum Steiner cut, which uses
$(\log n)^{O(1)}$ maximum flow calls and additional near-linear time. This
algorithm improves on Li and Panigrahi's (FOCS 2020) algorithm, which uses
$(\log n)^{O(1/\epsilon^4)}$ maximum flow calls and additional
$O(m^{1+\epsilon})$ time, for $\epsilon > 0$. Our algorithm thus shows that
deterministic minimum Steiner cut can be solved in maximum flow time up to
polylogarithmic factors, given any black-box deterministic maximum flow
algorithm. Our main technical contribution is a novel deterministic graph
decomposition method for terminal vertices that generalizes all existing
$s$-strong partitioning methods, which we believe may have future applications.
