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I may get to visit the Cerveny factory in Czech later this month when we visit our daughter and her family, assuming I can talk my pianist/violinist wife into spending a day of our vacation there! What size is the receiver on their BBb tubas? Will my European shanks fit?

My early 90's BBb took a standard shank, so I'm pretty sure they still would.

If you decide you want to try any of their F tubas, the older ones (can't speak for the new ones) use a receiver that is just a tiny bit smaller than your standard or "American" shank. Those mouthpieces will work fine but will just stick out a little more than usual. The common solution is either shave down the shank a tiny bit or cut the main slide a hair; the latter allows the use of any standard shank mouthpiece in any pitch setting.
Remember that on these horns, the "receiver" is really just the end of the leadpipe with a piece of nickle silver wrapped around it to give it strength.