Here's the answer from the MI Knowledge Base:
http://testdrive.mapinfo.com/techsupp/miprod.nsf/kbase_by_product/8A613772C77080D285256AA4006BFA62

"Width: {horizontal size in pixels} = {horizontal size in dialog units} * 1.5 +
6 (rounded to nearest integer -- .5 rounds up)
Height: {vertical size in pixels} = {vertical size in dialog units} * 1.625 + 6

This last formula does not include the title bar of the dialog, which may
change in height if Large or Extra Large fonts are used. The "+ 6" does take
into account the standard-width border around the edge of the dialog, however."

You call the API GetDEviceCaps() to findn out the size of the screen in pixels.

Bill Thoen wrote:

> If it is, then I'll amend the question to "How do I position a dialog flush
> with the lower right corner of the screen?"
>
> Ben A Greenberg wrote:
>
> > Isin't it dependent on the user's display resolution?
> >
> > Ben  Greenberg
> > GIS Coordinator
> > NAI MLG Commercial
> > 262-797-9400
> >
> > -----Original Message-----
> > From: Bill Thoen [mailto:[EMAIL PROTECTED]
> > Sent: Monday, July 21, 2003 10:46 AM
> > To: MapInfo-L
> > Subject: MI-L MB: Dialog Positioning
> >
> > Does anyone know the conversion factor between MapBasic dialog
> > units and pixels? I need to position a dialog on the screen
> > relative to the lower right corner of the screeen.
> >
> > --


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