In terms of simple physics F = V mu... If you double the contact area, then the pressure will halve (per mm2) so the friction per mm2 will halve. However, you have twice the area of contact patch so that cancels out the halved pressure. The conclusion is that basic friction is independent of area, it only needs vertical load and a co-coefficient. You can do whatever you want with the area from a stiletto to a surfboard, the friction force will be the same.
However life is more complex than simple physics. The most obvious point is that tyre rubber is adhesive, so if you double the area you double the amount of adhesion (gross approximation). So wide tyres do have more grip than thin tyres.
Another point is that the stiletto will dig into the surface causing interlock but that is also ignored in F = V mu
There are couple of threads on here with a lot more detail. Have a read of them and if you have question about the concepts I suggest you post in the relevant thread. (This is probably the only forum that encourages resurrection of old threads!)
The post by Ciro in this thread is seminal in f1tech (well it is in my mind) ....
viewtopic.php?f=6&t=9333
There are also some other similar threads ...
viewtopic.php?f=6&t=6330
viewtopic.php?f=6&t=8371
viewtopic.php?f=6&t=7734
viewtopic.php?f=6&t=6300
viewtopic.php?f=1&t=11603&start=60
viewtopic.php?f=6&t=12180
viewtopic.php?f=11&t=10276