Split-Key vanity address generation is a process that requires basically no trust from any party.
The main idea is, OP can create a vanity address without even knowing what private key it will actually belong to. Suppose you grab a random ECDSA keypair and save the private key for yourself. You can then issue a request for a vanity address to be created, by supplying the public key form that keypair, and mention your desired prefix. OP will then be looking for the vanity address by bruteforcing random ECDSA private keys and can get his corresponding public keys, add them to the provided public key, and proceed normally with SHA, RIPEMD and base58 until he receive the desired pattern. Then he will give the private key found to you. Then you can add the two private keys in order to get your vanity address. The best thing about it is that the person looking for the solution won't know what the resulting private key is! This means that you can outsource your vanity key generation without needing to trust anyone.