This bug affects only situations where padding is added to HTML and/or BODY is given a specific width and centered on the page. In these scenarios, containment and positioning are miscalculated. Both relatively- and absolutely-positioned draggable elements are affected.
The miscalculations vary depending on the combination of CSS used. Use this demo page to toggle each CSS setting to see how the draggables are affected...
Note that Draggable ''does'' handle BODY borders and padding correctly. It is only HTML padding and BODY margins that throw it a curve.
This demo uses jQuery 1.9.0b1 (to see if it helped), but the Draggable issues existed with previous versions of both jQuery and UI as well.
I found this bug because I have a widget for complex application/page layouts. Instead of adding unnecessary wrapper-divs to 'simulate' the BODY, I applied CSS directly to the HTML and BODY elements. This CSS works fine and is consistent across all browsers, even IE6, so it is perfectly valid CSS.
Everything else on such pages works normally, including my own size and position calculations for absolutely-positioned children of BODY, so the data returned by the browser is accurate and consistent.
This is admittedly a rare bug, but a bug nonetheless. I'll be happy to modify the linked demo page if it would be helpful to trace the problem. Or simply download the page - it is fully self-contained.