I stand corrected, for some reason I had a brain fart, SORRY guys.
Ok, let me see if I can get this correct this time with the help of Sheldon Brown's site to refresh my pea brain.
A 17 mm wide rim can accept a tire from 25 to 37 max. The Shimano rim could go up to a 44, but since I have these rims I think 44 is pushing it a lot since I run 25's on them currently and they're just fine even though supposedly the minimum width they should be a 28 which is the largest size that would fit on my bike anyways, a 44 in my opinion on that rim, I just can't see how that rim could handle it without issues with too much tire roll due to the tire's width vs the tire's height which would then act like a lever and on sharp fast turns could cause the sidewall to collapse and roll off the rim. I could be wrong about the Shimano since I never actually tried to fit a 44 on it, but from 40 years of experience eyeballing this sort of thing I just can't see it, I think a 38 would be the max that would fit on it comfortably, maybe a 40 but again I have my doubts.
Like Alfena said you can't just put tires on and go even if they fit the rim because they may not fit on the bike either due to brake clearance, top and/or sides, or fork. The rear usually has more room available vs the front but only by one tire size more usually but not always, it may be the same as the front or it might handle 2 or 3 sizes larger. The bike manufacture, or the bike shop, should be able to tell you what the max tire size that will fit on the bike as they equipped it.
All this tire size thing is subject to manufactures interpretation of tire size, one tire company that makes a 32 could fit in my bike and another would be way too tight even more so than a normal 32, so there is some trial and error involved to make sure you find the right tire. In my bike's case it's the clearance distance from the sides, even if the calipers are open I wouldn't be able to slip in a 32. If the tire is built a bit larger than the listed 28 (for example the max that will fit my bike) say it actually measure 29 though it's marked a 28, it will fit howbeit tight. So if a manufacture say's their bike will only accept a 28, like in my case, they usually build in some room for error to take into consideration manufacturer's failure to make sure the tire meets the sidewall listed tire size.
