Mukou gawa vs. Mukougawa

[Maka]

I've seen the title of the movie written both ways on the wiki, so which one is right? Mukougawa tends to get more results on google.

[Miyuka]

Mukougawa is correct. The second part of the compound word, kawa (側 "side"), is affected by the rule of rendaku (連濁 "sequential voicing") and became gawa with g-; it is customary to treat a word with rendaku as a true compound, rather than a phrase.