NASA started the process for the ISS as a shuttle delivered components system.
Spacelab was designed for maximal size for the payload bay, for any given length within the bay; in other words, you're not loading larger diameter modules in a shuttle cargo bay. The lab habitation modules were 4.12m diameter, 2.7m long.
Note that larger modules could and were built to fit in the space shuttle payload bay's 4.6x18m capacity, but Spacelab was intentionally spaced away from the walls.
Modules of up to 4.477m diameter have been built and launched on the shuttle; all the modules I've been able to find show the same 4.89m (16') bay width limitation in mind, and the shuttle payload design limit of 4.6m (15').
Note that the Delta IV has been proposed for future launches; present non-shuttle launches of modules to the ISS have all been on Soyuz-U and Proton-K rockets. The Delta IV has a 5m diameter.
The Falcon 9 has carried components to orbit in the trunk of the Dragon Cargo Capsules; such components have been smaller, to match the roughly 3.5m internal limit of the 3.7m diameter trunk.
Both the Falcon and Delta IV can carry wider payloads; the Falcon 9 fairing is capable of a shuttle-loadable payload inside it's 5m diameter, 13m long fairing.
The Delta IV likewise has a 5m payload fairing. Either could, in theory, carry a wider fairing; current components in process, however, do not require such capacity.
Further, the largest limit at present is primarily the lack of lift capacity, more than the volume lifted. The Falcon could carry most of the extant components, for example, but would be near its capacity limit. The Delta IV would be overloaded by many of the current modules. The Heavy Variants of either could carry larger modules, but given the weight and volume ratios, those larger modules are likely to be longer, and fit in the standard extant fairings, and to be in the 4.4m to 4.7m diameter range.
Due to the common carriage requirements between Spacelab and ISS, components had to fit in the shuttle bay. Given current launcher needs, launchers only need to carry components that were designed to fit the shuttle's bay.