Thanks, Ragnar.
Well... I did know that much...
Here is what I have tried:
Positioning windows in two monitors and closing Maya. The windows (Outliner, etc.) would reappear in the primary monitor docked in the top right corner.
Editing windowPrefs.mel values.
E.g.
windowPref -topLeftCorner 0 1650 -widthHeight 250 400 -parentMain true outlinerPanel1Window;
After Maya restart the Outliner window would still appear docked in the top right corner with the values overwritten as follows:
windowPref -topLeftCorner 0 1350 -widthHeight 250 400 -parentMain true outlinerPanel1Window;
Ah, to put the numbers into context, I am running two monitors @ 1600x1200.
I have also tried setting -parentMain to false with no noticeable effect. All changes to the file were made with Maya closed.
Another thing, how would I cause certain windows (Outliner, Hypergraph, etc.) to open automatically (in their correct positions obviously...) upon Maya start-up? And it would also be good to have the channel box, shelves and toolbars in the secondary monitor. As I understand all these windows are invoked in Maya via MEL procedures. My meek tampering with userRunTimeCommands.mel is yet to bring any usable results