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I received a transaction from an exchange. It has 30 outputs, the fee was - according to blockchain.com - roughly 18k sats. Is this the fee per output or for the entire transaction? Is it cheaper - and if so why - to send transactions with multiple outputs?

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Is this the fee per output or for the entire transaction?

The fee is per transaction not per output. In the network data it is simply sum of input amounts - sum of output amounts.

Is it cheaper - and if so why - to send transactions with multiple outputs?

The creator of a transaction is using the fee to bid in an auction of space in the next block. Therefore the fee is based on the size of the transaction in bytes (or in vbytes for segwit transactions). This is sometimes called the weight.

Since every transaction needs a header and at least one input and usually a change output, you save on repeating the byte sizes of these by combining many commercial transactions into one Bitcoin transaction.

HIOOOOOOC "weighs" less than HIOC+HIOC+HIOC+HIOC+HIOC+HIOC. Therefore it costs less.

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