This post summarizes how contract ids are generated:
…contract IDs are built from a cryptography hash (called a discriminator ), computed during evaluation via a deterministic derivation scheme from an initial high-entropy number (called a submission seed ) picked at submission time.
…the derivation scheme guarantees that if the submission seed was never used before, (1) the discriminators of contract IDs created by the transaction are globally unique and (2) that no information about the transaction can be inferred from one of the discriminators given alone.
Yes, the contract ids are intended to be globally unique, even across a network of ledgers. That is achieved through entropy, similar to other UID schemes.