Recently I have heard about zero balance accounts with a nonce of zero appearing on the blockchain.

My understanding is that any account that has been used in a transaction must have a nonce greater than zero. This would include zero balance addresses that have received funds and were later emptied.

How can accounts with a nonce of zero appear on the blockchain?

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    The question is accurate but for clarity, an account's nonce is only incremented when it originates a transaction. When the account is a receiver, its nonce doesn't change. – eth Nov 19 '16 at 8:19

When you send a zero value transaction to an account that does not exist. The same works for zero value creates (both through transactions and the CREATE opcode) as well as CALLing in to an account that does not exist.

This is a mistake, a flaw in the protocol. One we want to fix in the next upcoming hardfork.

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    Would you be able to expound or shed more light about the flaw or flaws and challenges here? Thanks. – eth Nov 19 '16 at 7:55

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