  We study the fractional quantum Hall effect in three dimensional systems
consisting of infinitely many stacked two dimensional electron gases placed in
transverse magnetic fields. This limit introduces new features into the bulk
physics such as quasiparticles with non-trivial internal structure, irrational
braiding phases, and the necessity of a boundary hierarchy construction for
interlayer correlated states. The bulk states host a family of surface phases
obtained by hybridizing the edge states in each layer. We analyze the surface
conduction in these phases by means of sum rule and renormalization group
arguments and by explicit computations at weak tunneling in the presence of
disorder. We find that in cases where the interlayer electron tunneling is not
relevant in the clean limit, the surface phases are chiral semi-metals that
conduct only in the presence of disorder or at finite temperature. We show that
this class of problems which are naturally formulated as interacting bosonic
theories can be fermionized by a general technique that could prove useful in
the solution of such ``one and a half'' dimensional problems.
