However, our brain is an incredibly complex and really cool organ. It is so cool, it can restore itself. The same studies prove that it takes the brain just a few months to regain its volume after a person stops using alcohol or drugs.
How does it manage to do this?
The development of addiction takes place in the limbic system. It is our ‘ancient’ brain, and it is difficult for us to consciously control it. It is the prefrontal cortex — the neocortex — that controls our behavior. While a person is consuming, less and less neural connections are being used in the cortex. And everything that is not used by the brain atrophies, thus, the volume of grey matter decreases.
When a person quits, they no longer give way to the impulses of the limbic system. Step by step, they are regaining conscious control over themselves. The prefrontal cortex is being used more and more, and new neural connections are being formed in it. The neo-cortex increases to its normal size, just like in non addicted people. But that is not the end of the story.
This happens due to neuroplasticity, the ability of the brain to change in response to experience and recover from damage.
The cortex recovers and continues to enlarge

This scheme is taken from the study on changes in the brain of addicts. The left part shows a decrease in grey matter volume depending on the years of use. The right part presents an increase depending on the abstinence period.
Grey matter volume in the prefrontal cortex is restored to normal in about 35 weeks. But even after that, the cortex keeps increasing further.
Grey matter volume in those addicts who have maintained abstinence for more than 35 weeks exceeds grey matter volume in those who have never had addiction issues.
So far, the scientists are not able to give a distinct answer to the question why the prefrontal cortex keeps enlarging and becomes thicker than in normal samples. However, the researchers have an assumption that it happens because the addicted have to maintain tighter control over their emotions and impulses.