These can be hot or cold. They are wallets that are kept by a custodian, typically, an exchange.
If you open an account on the Coinbase exchange, for example, they will create a wallet for you and give you access to it via their account credentials (e.g., username and password). It’s completely transparent and therefore convenient. Most exchange users don’t even realize that the exchange is their wallet custodian.
Some custodians, like Xapo, keep a copy of your wallet in cold storage in a Swiss mountain (that’s not a joke). It’s extremely safe, but very slow. Definitely not the right solution for Graypay users (!), so we’re going to focus on hot custodial wallets.
Remember those 12 words that were generated when we created our MetaMask wallet? When you create a hot wallet with a custodian, you also get 12 words! Handy. It turns out that you can use those 12 words to import (or access) your custodied wallet from within MetaMask. All you need to do is “Import using account seed phrase” instead of logging in.