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Wider tire = a more ovaly contact patch that has pressure more evenly distributed throughout. The key to grip is to have the largest, most homogeneous contact patch possible. A wider tire helps with the latter. This means more grip. A wider tire will also generally reach peak grip at a smaller slip angle because of increased lateral stiffness (hence the concept of wider tires breaking away more suddenly) which means BETTER turn in (assuming identical side walls). You will have to fight it more (i.e. heavier steering), but that shouldn't be an issue with power steering.
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