  Employing a recent technology of tree surgery we prove a
``deletion-constriction'' formula for products of rooted spanning trees on
weighted directed graphs that generalizes deletion-contraction on undirected
graphs. The formula implies that, letting $\tau_x^\varnothing$, $\tau_x^+$, and
$\tau_x^-$ be the rooted spanning tree polynomials obtained respectively by
removing an edge in both directions or by forcing the tree to pass through
either direction of that edge, the vectors $(\tau_x^\varnothing, \tau_x^+,
\tau_x^-)$ are coplanar for all roots $x$. We deploy the result to give an
alternative derivation of a recently found mutual linearity of stationary
currents of Markov chains. We generalize deletion-constriction and current
linearity among two edges, and conjecture that similar results may hold for
arbitrary subsets of edges.
