The lighting appears to be a single large roundish softbox (like the Elinchrom Octa) immediately behind the photographer/camera in most of the images. The shadow pattern is very similar to what you'd get with a ring light -- the outlines are darker than the center and there are no obvious shadows under the eyes or nose, etc. -- but softer. There is a vertical stripe "missing" from the lighting pattern, though -- and that'd be the photographer's position. The stripe is rather rectangular, though, which leads me to believe that the photographer has placed a gobo either behind -- or perhaps in front of -- the camera in order to keep the reflection out of the subjects's eyes. At least one picture, though (Paris Hilton) seems to have used a similar setup with either a large square softbox (Quadra, if we're actually in Elinchrom country) or two vertically-oriented rectangular softboxes (still huge) placed either side of the camera.

The camera is definitely a view camera, very likely an 8x10 with a 210mm lens going by the perspective -- which makes these photographs essentially macro photos. The aperture setting could actually be quite small by 35m-format standards -- f/22 or smaller wouldn't be out of the question for the depth of field we're seeing.