Well, as big as I can get I suppose is the answer, but in reality just about any size at least 2" being the least dimension. Don't really want a 3/4" plank - but....
If you're looking for color variation I have these three pieces. All are air dried. (2013) I can't say if they are Burr Oak for sure so I will just call it White Oak. The picture of the single piece I just skip planed today to hopefully to give you a better idea of color variation The three pieces are roughly the same size as written on the tape.
Looking for more like this. I would not know if just a little burr oak was like this and very rare, but have seen some carvings/sculpture/turnings making use of the color difference between the sapwood and heartwood.
Lil’Mikey can’t help you with that, but it is beautiful species especially when it is true quarter sawn. I was able to get some from an arborist in Ohio a very long time ago as I have proposed ship lapped walls for a client of mine in their entertainment room in Charleston. I also proposed live oak because it is abundant in SC- look up “Angel Oak”. I ended up with 5 small left over pieces- gave a sample to the client for reference. These were all the sapwood sections.
The burr oak type that has heartwood and sapwood mix can be had, but you have to go across the pond for this species of Oak (English burr oak)- Teale & Sons Timber.