To allocate a task or responsibility to someone. The manager will assign the new project to the most experienced team member.
To designate or set something aside for a specific purpose. The teacher will assign a portion of the classroom for the art supplies.
To attribute a particular quality or characteristic to someone or something. The critics often assign great talent to the young musician.
To transfer (property, rights, or interests) to another, especially in writing; to convey. The landlord assigned the lease to a new tenant.