Is it permissible for the owner of livestock to agree with another breeder that the latter receives half of its offspring, while the mother remains with its original owner?

This format is not valid because the wage is unknown, and the wage must be specified to avoid ambiguity and uncertainty, due to the Prophet's (PBUH) prohibition of hiring a worker until his wage is made clear to him. The correct alternative is to hire someone to tend the livestock for a known wage, or for a portion of the sheep to be owned by the worker.