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There are two ways to go 'bigger.' Taller tires -- meaning tire/wheel combinations with a larger overall diameter -- will reduce your effective gearing, but increase your potential top speed in each gear (if you're currently hitting redline, but wouldn't benefit from shifting to a higher gear, or if you're in your top gear). In case that sounds like a benefit, I'll put it more simply: if your car is low on torque, a taller tire will make the situation worse. But if there are particular points on a particular track where your gearing is too short, taller tires can sometimes be a cost-effective way to address the problem. Generally speaking, though, it's almost always better to go to a shorter tire so that your gearing is reduced, and therefore gives you more effective torque.
(A note for future thread readers who might not understand tire sizing: A tire's overall diameter (23-27 inches, or thereabouts) does not correspond in a linear way to what diameter of wheel you're mounting the tires on (15, 16, 17 or 18). The tire's overall diameter is determined by the second number in a tire size, which indicates the percentage size of the sidewall, relative to the tire's width. With a 245/45x16 tire, the '45' is the sidewall size -- in this case 45% of the tire's 245mm width. A 245/50x15 tire would fit on a smaller-diameter wheel, but would be a larger-diameter tire, because 50% of 245mm is larger than 45%. A 275/45 tire would have a much larger overall diameter than a 245/45, because 45% of 275mm is larger than 45% of 245mm.)
The other factor in tire size is width. This is the big one. Wider tires change the shape and mechanical properties (and to a limited extent, the size) of your contact patch. They also allow you to lower your tire pressures (and increase the size of your contact patch) without running into problems with heat dissipation as quickly.
They are almost always faster on a track than skinnier tires, everything else being equal.
The exception would be on very low horsepower cars, where you're going to hit a trade-off point between the increased drag from the tire's contact with the track, as well as an increase of aerodynamic drag, since the car's frontal area with the larger tires is bigger, and more significantly: the increased rotating (and unsprung) mass of heavier wheels and tires. There's always a trade-off, isn't there?
But the general rule with tire width remains: wider is faster. If your car is 3000 pounds or less, and making 250 hp or more, then my opinion is that there aren't any tires in commercially-available widths that are going to slow you down. You're limited by what will fit on your wheels and in your flares (and also by the need for proportionate widths relating to your car's F/R weight bias), and that's about it.
Bigger can be worse. But wider is almost always better.
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