Will the size of the tire affects the grip? wider /= more grip?
We haven't really gotten into the physics of it yet in this thread, but grip provided by a tire is a very complicated subject. One of the largest factors is the contact patch; tire rubber has a non-linear coefficient of friction, which is to say if you put twice the weight on a tire, you're not going to get twice as much friction out. You'll get more friction, but an increasingly lesser amount the more you push. Ergo, the larger the contact patch, the lower the pressure per square inch, and the more grip. Yet this proves a logical hurdle, as contact patch is related to pressure- EG, a 325 and 195 tire are going to have the same size contact patch if both tires are at the same pressure and supporting the same weight. But we intuitively know that the 325 is going to provide better grip!
Which takes us out of the real of tire statics and into tire dynamics: tires deform. While cornering, the tires are not rolling straight ahead, but rather are canted at an angle compared to the actual motion of the car- this is called "slip angle" and you can google it for a better explanation that I can give. Essentially, the tire rubber is at rest when a patch first touches ground, but the longer it stays on the ground, the further out of true physics is trying to pull that rubber, until finally it violently snaps back into place (which he hear as squeal). A wider tire with a thin contact patch will displace a given bit of rubber less than a narrower tire with a longer contact patch, and can still provide grip at much higher slip angles.
There is a limit, though; you're only going to be able to get so much rubber on a given wheel before you're distorting it during installation. And additional rubber means additional weight (rolling unsprung mass!) which takes additional energy during acceleration and braking.
As mentioned above with the load to grip ratio, unless Dunlop changed the way tires work, it's another reason to take marketing materials with a grain of salt. Dunlop shows a linear relationship in the link below:
Because of the difference in shape of the contact patch, I've always felt a comparatively narrower size would put power down better for straight line acceleration. Never tested back to back, just theory. For maximum lateral grip a wider tires shape should be better. To add on to points made above, rim width will play a part with a tires distortion and is not something discussed as frequently. There will be diminishing returns for tire width if the rim width isn't changed as well. Narrower tires with additional slip also generate heat quicker, so depending on the compound and temperatures, may be better suited for Solo II competition.
Other note is that a wider tire / wheel combo can be more difficult to drive faster on. With the decrease in slip angle, maximum grip, will be achieved at a faster rate and also fall off at a faster rate. Closer to an on/off switch than a similar narrower combo.