  We investigate the combinatorial analogues, in the context of normal
surfaces, of taut and transversely measured (codimension 1) foliations of
3-manifolds. We establish that the existence of certain combinatorial
structures, a priori weaker than the existence of the corresponding foliation,
is sufficient to guarantee that the manifold in question satisfies certain
properties, e.g. irreducibility. The finiteness of our combinatorial structures
allows us to make our results quantitative in nature and has (coarse)
geometrical consequences for the manifold. Furthermore, our techniques give a
straightforward combinatorial proof of Novikov's theorem.
