Encryption in a Distributed PKI?
This sounds like the scenario of identity-based encryption, or IBE.

In IBE, the ‘root CA’, called the private key generator or PKG in this scenario, doesn't handle encrypting or decrypting messages directly, but does have to furnish Bob and Carol with their respective private keys.  As long as Alice knows the names Bob and Carol, and the long-term master public key of the PKG, Alice can send encrypted messages to Bob and Carol—even offline, without contact with the PKG.  Then whoever can convince the PKG that they are named Bob or Carol will get a private key to decrypt those messages.

Of course, the PKG is a central point of failure: anyone who can compromise the PKG can decrypt all messages.