  Motivated to find the answers to some of the questions that have occurred in
recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special
classes of grid graphs we started the investigation of spanning unions of
cycles, the so-called 2-factors, in these graphs (as a generalizations of HCs).
For all the three types of graphs from the title and for any integer $m \geq 2$
we propose an algorithm for obtaining a specially designed (transfer) digraph
${\cal D}^*_m$. The problem of enumeration of 2-factors is reduced to the
problem of enumerating oriented walks in this digraph. Computational results we
gathered for $m \leq 17$ reveal some interesting properties both for the
digraphs ${\cal D}^*_m$ and for the sequences of numbers of 2-factors. We prove
some of them for arbitrary $m \geq 2$.
