  We present a range of applications of localisation for constrained transports
for pairs of probability measures in order with respect to a lattice cone.
  These examples comprise irreducible convex paving for martingale transports
in infinite-dimensional spaces, irreducible convex paving for submartingale
transports, localisation of the Monge--Kantorovich problem, pavings for
harmonic transports, pavings for solutions of martingale problems.
  Furthermore, we consider approximating martingale transports and characterise
the polar sets in this setting, identifying them as the trivial polar sets --
the sets whose projections have vanishing measures. This provides a negative
answer to a question of Cox
