do they have a nucleus?
All cranial nerves have a nucleus. With the exception of the olfactory nerve and optic nerve, all the nuclei are present in the brainstem.
Cranial nerves
Grossly, all cranial nerves have a nucleus. With the exception of the olfactory nerve (I) and optic nerve (II), all the nuclei are present in the brainstem.

where do the cranial nerves branch off the brain The terminal nerves; olfactory nerves and optic nerves emerge from the cerebrum, and the remaining ten pairs arise from the brainstem, which is the lower part of the brain. what do they do? They relay information between the brain and parts of the body.
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Cranial nerves [SEP] Nuclei
Because each nerve may have several functions, the nerve fibres that make up the nerve may collect in more than one nucleus. For example, the trigeminal nerve (V), which has a sensory and a motor role, has at least four nuclei.