There have been a few, but for practical purposes most BMX chainwheels are produced with the larger bore. It makes it easier for retailers to stock one product that will fit a variety of cranks with an adapter.
I don't recognize that spindle. If you know the maker, you might want to search the web for a euro conversion BB kit.
It's some no-name stuff I bought for cheap from a German eBayer. But my measurements are conrirming that it is the same size as a 1-piece american (which I also happen to have), eccept that it's in three pieces - I hope I am making sense. It uses the same (american) BB as the 1-piece crank.
OK, so now I gots to order that adapter. It sucks that Dan's Comp has such shipping policy, that a $3.99 item will cause me a $38 shipping charge. That's nuts... but I scanned the 'net and couldn't find anyone else selling these adapters. Yet. More scanning ahead.