Block.one is developing the EOS software now that block producers will then create a blockchain on after June 1 2018. Just like with Bitcoin, there will be one dominant chain, but then certain block producers might want to create their own fork of the main chain to set up their own projects. In which case they'd take a snapshot on Ethereum of everyone holding the EOS ERC20 tokens, and map them onto their own chains too. Just like when you hold Bitcoin, you also get Bitcoin Cash, Bitcoin Gold, and whatever other forks there might be in the future. That's how I understand it.

There's already a fork like this happening right now, it's called the Xenon Network, and they're planning on distributing to everyone for free on the basis of Bitcoin and Ethereum holdings.

Pretty exciting isn't it!