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I know people who've run 25mm GP4000s and 28mm GP4000s during TCR.
Evan used them in TABR: "Continental GP 4000s (tires replaced mid-race)"
Paul Buckley used Schwalbe Ones (the older ones, I think S-Ones maybe in 30mm?)
"Continental Gator Hardshell 28” tires performed superbly and 1 set of tires lasted the whole Trans Am. Gator Hardshell tires have re-enforced sidewalls unlike the regular Gatorskins. 1 puncture during the Trans Am when I got a drawing pin through my rear tire in Cowdry, Colorado. I put tubeless sealant in my inner tubes and also used Mr Tuffy tire liners."
BurlyCross used Schwalbe One tubeless 28mm
https://burlycross.wordpress.com/2015/08/17/salsa-colossal-tcr/Chris Herbert
"tubeless (Schwalbe Pro One) tyres, despite only being 23mm"
"For the actual race I’ll be using 25mm tyres, but they’ll definitely be Pro Ones"
https://brbrn.wordpress.com/2016/04/04/3-down-starting-to-come-together/Ed Pickup on Duranos:
https://edwardpickup.com/2013/12/05/gear-review-transcontinental-kit/TABR has much better roads than TCR so beware of TABR tyre choice, but still:
https://transambikerace.com/racer-steeds/Lael Wilcox TABR: "Hutchinson Sector 28 tubeless road tires"
"I tried tubeless tyres but they’re just to tight causing nervous break downs during mounting and I don’t want to risk getting a serious issue with one of the tyres and not be able to get it back on the rim while being exhausted and having no power in my arms and hands. Fast and proven quality for my tyre choice: 28mm Continental Grand Prix 4000 S II Race tyres will get me across Europe as they have brought millions of others to their destination too. Probably the most sold tyre in the past three years. I used to ride 23mm width tyres, but 28mm gives me much more control and comfort with a loaded bike as I experienced after buying the Mason Resolution"
https://www.cyclingacrosstheworld.com/gear-list-transcontinental-race-2016/
Yes, there is a wide range used. Schwalbe Pro One tubeless and Conti GP4000 (tubes) are probably the most common. I've had a tyre failure in a big ride using each of those so won't give any recommendations!
Same with width. I'd guess 25mm probably most common but plenty of 23 and 28mm and a few fatter ones.