In a world where ESP is common, only three people have them at the highest possible level. Those three are the special ESP team, The Children. The Children work for BABEL, a special ESPer organization committed to stopping crimes before they happen. Kouichi Minamoto is assigned to watch over them, and he'll need to, because three superpowered ten-year-olds are a problem on their own. 
 
(Source: Sentai Filmworks)

An OVA that takes place during the manga's middle school storyline.

In the future, as people with ESP increase in numbers, so does the possible good and evil they can cause to society. The Japanese government establishes of the Base of Backing ESP Laboratory (BABEL), a special esper organization tasked with dealing with situations that can't be resolved by ordinary means, including dealing with espers engaged in criminal activity. Prodigy Kouichi Minamoto is assigned by BABEL to the task of supervising the most powerful espers in the country, a trio of gifted but mischievous young girls known as "The Children". 

The Children and Minamoto must deal with several enemy organizations, each with conflicted views regarding the role of espers in the world, including "PANDRA", a cadre of rogue espers determined to wage war against the rest of mankind; "Black Phantom", a mercenary organization who brainwashes espers into living tools of destruction; and the "Normal People", composed solely of non-esper individuals who view espers only as a threat to be vanquished. 

(Source: Wikipedia) 

Included one-shot: 
Volume 1: Zettai Karen Children (pilot)

You don’t have to be psychic to know that Hyoubu Kyousuke is trouble waiting to happen, but having psychic powers of your own may be your only chance if you want to stand against him. One of the most powerful espers on the planet, Hyoubu's incredible range of abilities extends as far as controlling his own aging process, and the potential strength of all his talents combined is so terrifying that he wears a device that limits their use except in cases of extreme emergency. The time is coming, however, when Hyoubu will need to unleash everything he has. Because sometimes it takes a villain to do what heroes can’t, and as the leader of the secret organization PANDRA, Hyoubu's dedicated his life to fighting those who would entrap, enslave, or kill anyone with psychic powers. Now PANDRA itself is in danger and, to combat that deadly threat, the gloves and limiter are coming off! 
 
(Source: Sentai Filmworks)

Summary of the Zettai Karen Children TV series.

Hayate Ayasaki's life wasn't great, but when he loses the job he used to support his good-for-nothing family, and his deadbeat parents sell him to the Yakuza for cash, it really hits rock bottom! Faced with having to pay off the huge debt before he's converted into black market organ parts, a desperate Hayate decides to kidnap oddball heiress Nagi Sanzenin for ransom... but when even that goes wrong and he accidentally ends up rescuing Nagi from other kidnappers, it turns out that Hayate is the bodyguard that Nagi has been looking for! So now he's the Sanzenin family's butler, and… maybe… it might be the start of a potential romantic relationship… assuming Hayate can survive the on-the-job training, of course. 
 
(Source: Sentai Filmworks)

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