Salutations!
The large division of the brain that deals mainly with sensory and motor relays centers is: ------
The large division of the brain that deals mainly with sensory and motor relays centers is: forebrain. The forebrain in the further most portion of the brain, that includes cerebral hemispheres, thalamus, hypothalamus, higher vertebrates. These are the leading controls of sensory and motor relays etc.
Hope I helped :D