Shorter Chains in blockdata Assuming two blocks are published at exactly the same time, a race for the next block to be added to one of them begins, which eventually one chain will eventually win. 

My question: will the shorter chain still be published? Does the network still syncronize the shorter chain, i.e. does every client contain a copy of not only the longest chain, but all (for lack of a better word)  "sidechains"?
If so, are there any conditions as to what will be syncronized beyond block validity?

Thanks in advance!
will the shorter chain still be published?


Published -- no. However, if the stale tip was previously the best tip, it will be stored in a Bitcoin Core node implementation according to the source and other nodes can retrieve it up to a certain point in time. The time limit is imposed to avoid fingerprinting.


  Does the network still synchronize the shorter chain.


No, the node only ever extends the active chain.