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How wide a wheel should I run?

Modern radial tires will deliver the highest lateral and longitidinal grip when the tread area is fully supported. The basical rule is 1:1
Meaning wheel width should be the equal to or slightly greater than the actual tread width. This is not the casing width or the number stamped on the tire. It is the actual width of the tread.
OEM's have been selling cars with 1:1 fitments for almost 20 years. Despite this fact, many tire manufacture websites still warn against running wheels that are 1:1 with tread width. These conservative recommendations are made despite those same tire manufacturers working directly with OEM's on tires specifically for performance models with 1:1 fitments. Use your own judgment :)

Increased tension on sidewall reduces deflection betwen wheel angle and tread contact patch angle. This improves steering repsonse and precision

Increased air volume. Everything else being equal, a wider wheel will contain a larger air volume which heps reduce temperature swings in high performanec driving. It also lowers effective spring rateof the tire which generally improves grip.
Spring rate of the tire?  Yes, tires have a spring rate and it is largely undamped. The increased air volume allows a lower pressure to carry a given vehicle weight. The benefit here is that the contact patch loading per square inch decreases. This allows the tread area to confrom to surface irregularities better, which increases grip.

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