From what I, understand they're like notes that can be any denomination.
You would want to manage them so you can make most amounts with small remainder in change, right?
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Yes, correct; UTXOs can be any size. All are denominated in BTC.
1 bitcoin = 1 BTC. The smallest denomination is one satoshi, 1 sat, or 0.00000001 BTC.
If you have any bitcoin in a bitcoin wallet that has an on-chain bitcoin address, then you already have a UTXO. The bitcoin in your wallet is Unspent, and it is comprised of other UTXOs having sent bitcoin to your wallet so it is their Transaction Output that makes your address have a balance.
When you go to spend your bitcoin, your wallet will add up enough of your UTXOs in your wallet that cover the amount of whatever you're trying to spend (plus a transaction fee). The more UTXOs that are needed to cover that output you are trying to make will increase the overall "size" of the transaction.
I could go on and on about it, but I'd rather not put out any incorrect information. It's better to learn about it yourself. It's easier for me to understand how transactions work by looking at how they appear graphically in http://mempool.space.
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