if transactions were moved "off-chain", would the mainchain's blocks get the fee

[stslimited]

If transactions were moved "off-chain", would the main blockchain's blocks get the fees included in the blocks?

if so, how.

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[gmaxwell]

First you should answer "what does the bitcoin blockchain need to exist for?"— if there really are no transaction of any kind at all, then there is no reason for it to exist.

Most (all?) discussion about off-chain transactions still has transactions happening on the chain— just not all of them.  In those models network security is funded by the fees on transactions that happen on the chain and not (directly, at least) by ones that happen off of it.

(There are other motivations for transaction fees possible too— things like fidelity bonds... but in any case— I think we need more information to discuss your hypothetical future in any detail)

[TradeFortress]

Not all transactions will move off the chain. I would assume that at least for now people want to settle large transactions directly. Things like small transactions definitely will happen off the chain as long as the block size is not unlimited.

Eventually Bitcoin may move to a model where off chain networks pay large miners for insurance against double spending and then allow large transactions to be made on the Blockchain, without most people waiting for confirms if it is signed by a trustworthy entity.