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UTXO is an output transaction from someone to you (or anyone) and it stays unspent until it is used as transaction input.
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It takes as many UTXOs until it can cover for the whole of your transacion. If sum of UTXOs is bigger than what you want to spent, part of it goes back to you as another UTXO.
Actually I am not sure now, whether it works like I described (takes only as many UTXOs as necessary) or it takes all UTXOs and use it as input. Can you clarify this to me? Thanks.
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Wallet basicaly looks up for current transaction fees on blockchain and picks such transaction fee which enables you to process transaction with enough speed. Transaction fee = Input - Output.
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The privacy increases with increasing number of inputs and outputs of transaction.