Does rim width affect what tire size I can use

Pa's Toy said

Did so but received conflicting advice.... for example one thread spoke about a general rule of thumb of a tire width being no more than 2 inches more than the width of the rim. Other sites disagree with this ratio. Others suggest that 185/75r/14 will fit on a 4.5 but anything wider should be on a 5.5...thought I'd ask people with more hands on experience with these sorts of things

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You can't use a "rule of thumb" that only considers rim width and tire width. The sidewall height has A LOT to do with how much tire can overhang the rim.

For example, a 275/60/15 has an ~11" section width and can be mounted safely on a 15x7.5". A 275/35/18 on the other hand still has an ~11” section width, but requires at least an 18x9” rim.

That’s an extreme case because of the different rim diameters, but even with the same diameter rim the height of the tire has a significant effect on the width of tire that can be mounted on a particular rim.

All tire manufacturers post their minimum and maximum recommended rim widths for each tire.