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Will eth nodes be able to broadcast multi transactions signed by different but correct nonce in a same time?

example: there are 10 nodes, I broadcast 10 signed transaction to every node.

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Yes, that should be possible.

It's just that the tx with nonce 11 for example, will be kept in the mempool until all the transactions with lesser nonces will be accepted.

Also, to avoid ddos-ing, I expect the nodes to keep the transactions in their mempool for a very limited amount of time (if at all) for nonces that are far away from the next expected nonce.

You can actually broadcast even 2 (or more) different transactions with the same nonce (as long as none is accepted).

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