In ancient times, 't Hooft studied the mesons in QCD 1+1 [1] to illustrate the power of the large N limit [2] in the light-cone formalism. Recently some generalisations of the 't Hooft model have been studied, which retain a remnant of transverse degrees of freedom, based on a dimensional reduction of QCD to 1+1 dimensions [3,4,5,6,7,8,9]. In this collinear approximation, quarks and gluons are artificially restricted to move in one space dimension, but retain their polarization degree of freedom. In this lecture, a problem which in principle involves a large number of partons will be addressed in the context of the collinear model at large N . For light-cone quantisation, large numbers of partons are synonymous with small Bjorken-x. The example treated here 3 is the quark distribution function in a heavy meson, which is supposed to exhibit a version of Regge behaviour at small-x. The central idea involves high light-cone energy boundary conditions on wavefunctions -ladder relationswhich typically connect Fock space sectors of differing numbers of partons. The same ideas carry over to 3 + 1 dimensions [10].We start from SU (N ) gauge theory in 3 + 1-dimensions with one flavour of quarks. If we pick an arbitrary fixed space direction x 3 and restrict ourselves to zero momentum in the transverse directionsfor the gauge and quark fields, one finds an effectively two-dimensional gauge theory of adjoint scalars and fundamental Dirac spinors with action], D a = ∂ a + iA a , dx 1 dx 2 = L 2 , g 2 =g 2 /L 2 , andg is the four-dimensional coupling. The twocomponent spinors u and v are related to Ψ by