  Simplicial formal maps were introduced in the first paper, (math.QA/0512032),
of this series as a tool for studying Homotopy Quantum Field Theories with
background a general homotopy 2-type. Here we continue their study, showing how
a natural generalisation can handle much more general backgrounds. The question
of the geometric interpretation of these formal maps is partially answered in
terms of combinatorial bundles. This suggests new interpretations of HQFTs.
