Which of these statements describing cranial nerves with parasympathetic outflow is accurate? which of these statements describing cranial nerves with parasympathetic outflow is accurate? postganglionic axons of cranial nerves iii, vii, and ix travel with axons of the vagus nerve (cranial nerve x) to their final destinations. cranial nerve ix, which synapses in the otic ganglion, promotes secretions of the sublingual and submandibular glands. cranial nerve vii, which synapses in the pterygopalatine ganglion, regulates nasal secretions and tear production. cranial nerve iii promotes pupil dilation and secretions of the submandibular gland.