  High transition temperature (high-Tc) superconductivity is associated with
layered crystal structures. This work considers superconductivity in ultra-thin
crystals (of thickness equal to the transverse structural periodicity distance
d for one formula unit) of thirty-two cuprate, ruthenate, rutheno-cuprate, iron
pnictide, organic, and transuranic compounds, wherein intrinsic optimal
(highest) transition temperatures Tc0 (10 - 150 K) are assumed. Sheet
transition temperatures Tcs = {\alpha}Tc0, where {\alpha} < 1, are determined
from Kosterlitz-Thouless (KT) theory of phase transitions in two-dimensional
superconductors. Calculation of {\alpha} involves superconducting sheet carrier
densities NS derived theoretically from crystal structure, ionic valences, and
known doping, a two-fluid model for the temperature dependence of the
superconducting magnetic penetration depth, and experimental data on KT
transitions; {\alpha} is on average 0.83 (varying with standard deviation
0.11). Experiments on several thin crystal structures of thickness dF
approaching d are shown to be consistent with calculations of Tc0 from
microscopic superconductivity theory and with Tcs from KT theory, where the
presence of disorder is also taken into account; careful analyses of these thin
film studies indicate a minimum thickness dF \approx d for superconductivity
