CredSSP and kerberos credentials delegation

Hello,

please, would you be able to kindly provide some kind of a clarification
about the CredSSP and delegation of kerberos smart-card credentials (to TS
for example)?

I assume this:
the user is logged on by using smart-card (online by using DC)
the private key cannot leave the smart-card
the user then receives a valid TGT
then the client uses CredSSP to forward "his credentials" to a TS server.

and here comes the question:
what actually is forwarded to the TS server? is it the clients TGT together
with the session key to decrypt the TGT?

many thanks

ondra.