  Using the notion of tame regular $d$-path of the topological $n$-cube, we
introduce the tame regular realization of a precubical set as a multipointed
$d$-space. Its execution paths correspond to the nonconstant tame regular
$d$-paths in the geometric realization of the precubical set. The associated
Moore flow gives rise to a functor from precubical sets to Moore flows which is
weakly equivalent in the h-model structure to a colimit-preserving functor. The
two functors coincide when the precubical set is spatial, and in particular
proper. As a consequence, it is given a model category interpretation of the
known fact that the space of tame regular $d$-paths of a precubical set is
homotopy equivalent to a CW-complex. We conclude by introducing the regular
realization of a precubical set as a multipointed $d$-space and with some
observations about the homotopical properties of tameness.
