Is it possible (as in allowed by consensus, not doable with today's software) to create a zero-output transaction in Monero? In other words, is it possible to create a transaction whose inputs are entirely used as fees and creates no new outputs?
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Yes, it is possible, and while I can't point at it right now, I know there's at least one in the chain.
user36303
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There are exactly 534 transactions with 0 output (block [1,1500000]), 511 of them being in the famous block 202612
Example:
Moroccan Engineer
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