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Apart from the limited transaction size in MB, which theoretically limits the maximum amount of money a transaction can handle, is there any standardized bound?

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There is no limit on the per-input, per-output, fee, or total amount transacted, apart from the fact that all numbers need to be valid BTC amounts (which means not less than 0 and not more than 21M BTC).

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Transaction outputs are the only place we specify amounts, stored as 64-bit unsigned integers. So we can specify maximum of 92233720368.5 bitcoins in an transaction output.

https://github.com/bitcoin/bitcoin/blob/ddfd79659e31a41de4e9b824767b766116798a90/src/amount.h#L14

However, there are per-output checks using bool MoneyRange(), when a new block is announced. This is more important, since it lowers the maximum amount that can be transacted to the 21-million figure.

https://github.com/bitcoin/bitcoin/blob/ddfd79659e31a41de4e9b824767b766116798a90/src/amount.h#L31

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