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I understand that each transaction, new pairs of keys are generated, usually derived from a master key say in an HD wallet. If your change for a transaction or received BTC Is in multiple UTXOs, are separate pairs of keys made for each?

Is my understand a bit wrong? Because when you receive BTC, do you generate a completely new address (from newly generated keys), or one tied to UTXOs? I imagine the former. If so, then do wallet providers to minimise the amount of UTXOs? Say that combine all the BTC in my wallet into one UTXO, with one set of keys far down the HD derivation path.

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You can have multiple transactions sent to the same address (address reuse), it is just not recommended as it is not good for your privacy. (In this case you have multiple UTXOs that can be spent using the same private key.) A chain observer can see your increasing effective balance at that address rather than you receiving funds to multiple addresses and those multiple addresses not being linked.

Because when you receive BTC, do you generate a completely new address (from newly generated keys), or one tied to UTXOs?

Newly generated keys from your HD wallet.

If so, then do wallet providers to minimise the amount of UTXOs?

Wallet providers do consider UTXO or coin selection when spending UTXOs. There is generally a trade-off between privacy and minimizing the number of UTXOs in your wallet (and hence the future transaction fees you will have to pay).

Say that combine all the BTC in my wallet into one UTXO, with one set of keys far down the HD derivation path.

You can always create a transaction that sends all your UTXOs to a single UTXO (UTXO consolidation) but as I said earlier this isn't great for privacy as a chain observer now knows all prior transactions and the total balance are associated with a single individual.

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