Hemihydranencephaly is a severe cephalic disorder characterized by complete or almost complete absence of the cerebral cortex with preservation of meninges, basal ganglia, pons, medulla, cerebellum, and falx. It is a special type of Hydranencephaly.
It is a very rare disease. As it stands, only 7 cases have been reported.
References
Hemihydranencephaly Wikipedia(Text) CC BY-SA