I have read most of the Zettai Karen Children manga to the beginning till the latest chapter of it so I know most of the story, but this Ova seem to be another story that does not related the manga itself.
The story started at BABEL HQ, where Minamoto came back from a trip and suddenly destroy their Main Frame Computer and bomb HQ without a reason. Luckily "the Children" is in school playing Volleyball with the others.
Yuri's Moe Panic
Well they receive the news about the bombing of Minamoto at HQ from their invisible guard"Barrel".
"Yeah! Its Wilson!!"
So Chief explain all the details to them and send them to a safe location since Minamoto Became a strong enemy, however things did not go the way they are.
new way to threat someone
Kauro and the others got kidnap and put them to sleep. When she wake up, Minamoto was there waking her up and make Kauro think that Minamoto was frame but she was wrong. Minamoto trick Kauro to hurt Aoi and Shino in the remote controlled Tank and show that Minamoto was under the Heavy Hypnotism of Phantoms Daughter.
After that Aoi and Shino are in bed rest because the shock that Kauro give them and Kauro was depress that Minamoto became her enemy. Then again Phantom try to break Kauro by using Minamoto but Kyousuke interfere her this time that make no other choice but to retreat. Kyousuke tell to them that Minamoto was the key to make Kauro "Queen" but since Phantom have him, She will become the new Queen of Esper in the Future.
To prevent that future to happen, Kauro must kill Minamoto to set the Future back the way is was before. Meanwhile Phantom gathering some esper from PANDRA and BABEL for her next act. At end Kauro agree to Kyousuke plan, Aoi and Shino Awaken from their shock and they get ready for the next battle.
At the Roof Top while the other BABEL and PANDRA fight Hypno Esper of Phantom, Kauro and Minamoto meet face to face. Phantom was suppose to enjoy to watching Kauro's Anguish suddenly spoiled by Sasaki interference. On the right time while Kyousuke battle against Nai, He use the Hypnotism that place on Kauro to play back the future scene were Kauro going to get shot by Minamoto. Because of that trhe Hypnotism on Minamoto have weaken a bit and Kauro use the Absolute Force to break it.
Well he die for a while but revived by Sasaki and Kyousuke. At end Minamoto get punish by Aoi and Shino for saying sweet words to Kauro.
The Animation is good and so so, it remain me of Conan with a little Index or Railgun fight scene. The part I laugh too much at the "Shadow Children" scene where they speak English and tell about the OVA and The second season of it at school, Its was really fun hehe. Well I just hope they can make the second season.
Here a little insight of the OVA