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From what I've read they are all over the place........some small, some medium(ala '59 R9) some fat with shoulders(but these'd be pretty rare as I understand).
I've picked this up as being within each individual run(300) of a CC.
CC1 and 2 have larger necks, my CC2 is .933 in the first fret. Yet I can manage to play it somehow. It must have just enough shoulders taken off as normally that's deal breaking territory as I have hand/arm issues and big fatty necks and me don't gel at all.
Ask around and pretty much someone will say that EVERY SINGLE CC has some in that run that have large necks. The neck tolerances are all over the place. The bad thing is, if you really want a particular CC due to whose it is, or looks, with the necks being a crapshoot, it's hard to play multiple ones to settle on the one with the nicest neck.
Of the ones I've owned and have played, CC3, CC6 had large necks but others have said they are slimmer ones. Just goes to show you none of them are alike.