Final answer:
Parasympathetic pre-ganglionic axons from the brainstem run to terminal ganglia near target organs, not to sympathetic chain ganglia, thoracic splanchnic nerves, or dorsal root ganglia.
Step-by-step explanation:
The parasympathetic pre-ganglionic axons originating from cell bodies located in the brainstem project to terminal (intramural) ganglia that are near or within the target effector organs. These preganglionic parasympathetic fibers, upon reaching the ganglia, release Acetylcholine (ACh) onto nicotinic receptors to activate the ganglionic neurons. This is in contrast to the sympathetic nervous system, where preganglionic fibers may synapse in the sympathetic chain ganglia, prevertebral ganglia, or adrenal medulla.
Therefore, the parasympathetic pre-ganglionic axons running from brainstem-located cell bodies do not run to sympathetic chain ganglia, thoracic splanchnic nerves, or dorsal root ganglia, but rather to pelvic splanchnic nerves and associated ganglia close to target organs.