Where does the split happen between Mai-Hime and Mai-Otome? I know that Mai-Hime and Mai-Otome are anime (and maybe manga) series that are related by have different plots. I was wondering if there is a certain point where they split (like FMA and FMA: Brotherhood) or if they are entirely different plot-wise. If they are different, how are they connected beyond being created by the same production company?
They're entirely different story wise, My-HiME is set more or less in our world while My-Z HiME (My Otome) is set in a fictional universe.

They are roughly connected by the character and their personalities that exists in both series, such as Mai's and Natsuki's rivalry, Natsuki's Same Sex Relationship with Shizuru (In My-Z HiME they are much more open, in My-HiME they only are open with each other about their feeling near the end) and Haruka hot tempered personality and malapropism with Yukino always correcting her.

Also both series portray the females being the ones with power having to also come to terms with their adolescence and love at the same time as controling this power. in My-HiME it was choosing to have power at the cost of the person the girl loved the most (the warning Natsuki gives Mai before she awakens her Child) while with My-Z HiME it was choosing to have power and never being with a male (explained by how the Y Chromosome will destroy the Nano Machines and thus Otome's can't have any relationship with men)