I'll leave you to discuss anti-roll bars. "A fat tyre putting down more rubber in its footprint does in theory have more mechanical grip, all other things being equal." But, other things (weight, tyre pressure) being equal a wider tyre doesn't have a bigger contact patch, it's just a different shape. (The illusion may occur because it's easier to see the width of the tyre than the length in contact.) This is true across the sum of the tyres at all times (disregarding hills and squat) but the distribution of contact area between the tyres might be affected, depending on camber, compliance etc. (This isn't anything to do with the relation between contact area and grip, which is genuine and not adequately described by classical friction.) Jonathan