When you buy bitcoin, do you send yourself the private key?
Generally, they transfer the BTC you bought to the address you specified.
how you get your private key
You don’t get it.
First, let’s talk about your wallet, that’s where you store your BTC assets.
If you use web wallets like https://www.blockchain.com or hardware wallets like Ledger, you do not have direct access to your private keys. They store the background of your private keys, for security and accessibility reasons.
For security reasons, a wallet may have several private keys. When you received some BTC, the next time you click on “Accept” button, the wallet may show you a different address. That’s because the wallet has generated a new private key and a corresponding new BTC address. Your private key wallet has all these addresses that it generated, and the total of your money in the wallet is the summed values of all these addresses.
When you send BTC, you only need to enter the destination, fee, and transaction value. And the wallet itself will decide which of your addresses it will send. And your wallet signs the transaction with the corresponding private keys.
Of course you can take lower-level control, generate the private keys and addresses yourself, sign and broadcast your own transaction to send your BTC out to someone, using Bitcoin Core or with a program you made yourself. That’s a technical topic.
When you buy bitcoin somewhere, like https://www.paxful.com they work pretty much the same way. When you bought BTC, you don’t get the private key directly. Instead, you can transfer the purchased BTC to an address you specified. A paxful wallet will then send the BTC to your address.
and how you can pass it on
You cannot transfer it, when you do not have its own private key. But you don’t need to. If you want to move your BTC assets, you can send your BTC to another wallet.
It may take some time to understand how BTC really works – Feel free to ask me any questions