Hi!
Dome theory in a nutshell:
1) The dome diameter is responsible for the position of UW-infinity. The larger, the further.
2) The usable angle of a dome has to be at least as wide as the maximum diagonal angle of the lens.
3) The center of the dome sphere has to be placed in the perspective center of the lense.
The above items are vital for a good image quality when using a WA lens. There may be a few changes to the rules above for FE lenses without causing too much loss in image quality.
For a true 180° diagonal FE lens you'd need a hemispheric dome. It works in most cases to use a misplaced dome with a narrow angle (e.g. a 120° dome that is placed closer to avoid vignetting).
The dome diameter determines the distance of UW-infinity. A txpicl value is between 30 an d 50 cm for most common ports. Depending on the focal length and the position of UW-infinity you get different areas of DOF. This is espexially important when doing half-half shots. It is also important for corner sharpness as DOF is the only way to compensate the bent image plain caused by the dome. A larger dome diameter extends the focus range anf the DOF. You'll recognize an increase in corner sharpness.
Having to make a decision between a smaller well placed dome and a larger misplaced one (wrong set of extension rings e.g.) I'd take the smaller well placed post in most cases for WA but maybe the larger one for FE (becaue if it isn't a hemisphere it's misplaced anyway). FE lenses tolerate misplacement of a dome far better than WA lenses do. Thsi is caused by the different way they're projecting an image.
You'll find a more detailled explanation here on Wetpixel when searching for the essay on Dome Theory written by Julian (also contains sample calculations and illlustrations).
Helge ;-)=)