  In this and the companion paper a novel holonomy formulation of so called
Spin Foam models of lattice gauge gravity are explored. After giving a natural
basis for the space of simplicity constraints we define a universal boundary
Hilbert space, on which the imposition of different forms of the simplicity
constraints can be studied. We detail under which conditions this Hilbert space
can be mapped to a Hilbert space of projected spin networks or an ordinary spin
network space.
  These considerations allow to derive the general form of the transfer
operators which generates discrete time evolution. We will describe the
transfer operators for some current models on the different boundary Hilbert
spaces and highlight the role of the simplicity constraints determining the
concrete form of the time evolution operators.
