Linking static libraries, that share another static library
Solution 1:
Static libraries should never include other static libraries (or third party code in general). A static library is just a bundle of .o files glued together. So if you have multiple copies of the same information, it's going to blow up.
Each static library should just have its own code in it. The final application is responsible for linking all the required libraries together (including libraries required by libraries). This way there is exactly one copy of each thing linked.
Solution 2:
This sounds like exactly the sort of problem CoacoaPods was created to solve. If you define pods for each of theses projects then Z should be able to determine and link against all of its dependencies all the way up the chain without introducing duplicate symbols.