Final answer:
The Bill of Lading is the document used to establish the liabilities of common carriers, serving as a contract and receipt for the shipment.
Step-by-step explanation:
The document used to establish the liabilities of common carriers is the Bill of Lading. This legal document serves as a contract between the carrier and the shipper, detailing the type, quantity, and destination of the goods being transported. It outlines the carrier's terms and conditions of carriage, including their liability for any loss or damage to the goods. The Bill of Lading acts as a receipt for the goods shipped and a document of title, signifying ownership of the cargo.