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So, when a miner (or mining pool) creates a block that they will attempt to solve, they create a special transaction (called the coinbase transaction). The protocol allows this transaction to have 0 inputs, and to have outputs that have a total value that is less than or equal to the total of the current block subsidy and all the transaction fees (unaccounted for value from the transactions) of all the transactions that the miner includes in the block when they build it.
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Danny, the way you have phrased this has raised a question in my head; what if the miners do not accept the fee as allocated to them by the transaction? Where do the unspent outputs get output to in this (unlikely?) situation? Perhaps this would simply be an "invalid block", although I am not too familiar with the innard of BTC to this level...