CZ operates a flight daily out of LAX with no stop service to CAN (Guangzhou-Baiyun, CZ's headquarter airport). Delta does code share with CZ on LAX-CAN. It is a long flight and does not get sold very well because CAN is too close to HKG. Delta's flights in and out of PEK are either very early in the morning (before 9:00am) or very late at night (after 10:00pm), which leaves no time for a connection within China. Therefore CZ is not very interested in doing code share with Delta on PEK route.
There are two airports in Shanghai area. SHA (Hongqiao) is a domestic airport like Tokyo NHD. CZ operates very limited amount of flights out of SHA because it is not one of its hubs. There is not CZ flight out of PVG so they don't code share with each other.