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Motivated to find the answers to some of the questions that have occurred inrecent papers dealing with Hamiltonian cycles (abbreviated HCs) in some specialclasses of grid graphs we started the investigation of spanning unions ofcycles, 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 theproblem of enumerating oriented walks in this digraph. Computational results wegathered for $m \leq 17$ reveal some interesting properties both for thedigraphs ${\cal D}^*_m$ and for the sequences of numbers of 2-factors. We provesome of them for arbitrary $m \geq 2$.

A spanning union of cycles in rectangular grid graphs, thick grid cylinders and Moebius strips