This is a quite complex question. I should recomend the book of Paul Haney on the subject. This book also tell that tire dynamics is sort of "secret" stuff, and that not even the drivers can speak freely.
I hope that HiRich should not get angry at me for bringing up a few corrections.
Surface pressure. I have been discussing this issue with both Haney and M Ortiz, and also been making a number of experimenting myself.
There is also a scool that tells that the tire pressure sould balance the footprint area, so that wider tires should not end up with bigger footprints.
there are a number of commets to all those mentioned statements.
I campared two size Avon slicks for foot prints with the same size diameter but different widths, and the area to width theory did not showed to be true. After speaking with some tire manufacturer, (even Avon), they agree to this but where not willing to discuss the matter to deepley. Construction and sidwall stiffness is a factor. But in general, wider tires do give moore foot print area. As ยต is a result from load per area, this in itself should give a wider tire better grip in about the same range as a load change from using another rollbar, its the same pfenomenon.
The wide tire also show another foot print pattern, beeing moore of an oval shape, shorter and wider. This give another slipfunction that favour cornering. Needs some drawing to show.
Wider tires have greater cooling area and may run softer rubber for the same condition.
Hysteresis.
This is very good explained in the Haney book. The grip become better with a slow recover rubber since it only create force against the "loaded side" of pavemant obstructions.
Its hard to separate the friction capacity strictley from other factors in the suspension system, but I get the point from the questioner.
Performing test to see what happens is a VERY complicateded task.
I better stop here I guess. However, ther are a few examples on my site with footprints.
http://hem.passagen.se/hemipanter/
Klick "Wheels and tires."
Goran Malmberg