What is the "major control centre(s)" for the autonomic nervous system?

As you probably know, both the autonomic nervous system differs from the rest of the nervous system in having TWO (not one) neurones between the CNS and the innervated structure - the pre- and postganglionic neurones.

In the case of the sympathetic nervous system (SNS) the preganglionic neurones are sit in the (intermediolateral column of the) spinal cord at the levels T1-T12. For the PNS, they sit in the III, VII, IX and X cranial nerve nuclei in the brain stem, and in the spinal cord segments S2-S4.

But what causes them to fire (i.e. where to the nerves come from that synapse with the preganglionic neurones)?

Firstly, there are some autonomic reflexes (e.g. sweating) that operate at the level of the spinal cord. So, the spinal cord could be called a 'control centre', but it's function is fairly basic, and so I don't think this is what was asked for.

The next level up can lay a definite claim for being a "main control centre" of the ANS: the brainstem reticular formation, which integrates and controls things like blood pressure, heart rate, respiratory rate, peristalsis, and the like.

A little higher up is the chief organiser of the ANS, and the most fitting structure for the title "main control centre" - the hypothalamus. This integrates and modulates the structures below into one coherent whole.

Finally, other centres, like the amygdala and even the cerebral cortex, can modulate the ANS, although usually via the hypothalamus. For example, seeing a dangerous animal raises your heart rate.

So, I would say that the main control centres are principally the hypothalamus, reticular formation and amygdala.Hope that all helps!