  In a series of four papers we determine structures whose existence is dual,
in the sense of complementary, to the existence of stars or combs. Here, in the
second paper of the series, we present duality theorems for combinations of
stars and combs: dominating stars and dominated combs. As dominating stars
exist if and only if dominated combs do, the structures complementary to them
coincide. Like for arbitrary stars and combs, our duality theorems for
dominated combs (and dominating stars) are phrased in terms of normal trees or
tree-decompositions.
  The complementary structures we provide for dominated combs unify those for
stars and combs and allow us to derive our duality theorems for stars and combs
from those for dominated combs. This is surprising given that our complementary
structures for stars and combs are quite different: those for stars are locally
finite whereas those for combs are rayless.
