There are all sorts of things to factor in here: tyre width (obviously), power, weight of the vehicle, torque, suspension set up, type of surface being driven on (ice tyres for example are very narrow to concentrate the weight over a small area).
Just bolting on a wider tyre isn't necessarily going to make you go quicker - the car will need to be set up to work with those tyres, if you've got wider tyres but can't get them up to temperature then you're not going to gain anything. Also an increase in tyre grip can lead to problems with transmission and driveshafts as suddenly the load going through these is increased too.
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