  Over $d$-dimensional Cohen-Macaulay rings with a canonical module,
$d$-cotilting classes containing the maximal and balanced big Cohen-Macaulay
modules are classified. Particular emphasis is paid to the direct limit closure
of the balanced big Cohen-Macaulay modules, and the class of modules of depth
$d$, which are shown to respectively be the smallest and largest such cotilting
classes. Considerations are then given to the interplay between local
cohomology, canonical duality and cotilting modules for the class of Gorenstein
flat modules over Gorenstein local rings.
