If you're looking for manga similar to Zettai Karen Children, you might like these titles. All recommendations are made by Anime-Planet users like you!
When high school student Ageha Yoshina finds a red calling card in an isolated, ringing pay phone, he believes he's merely stumbled upon the game 'Psyren', a curious urban legend. He initially intends to trade information about Psyren to the world's foremost fortune teller for a famous reward, but after his childhood friend Sakurako – who happened to possess one of the cards – disappears, Ageha rushes into the game's dangerous world to find him. Now trapped in a post-apocalyptic landscape and pursued by Psyren's deranged inhabitants, Ageha must fight to survive and unravel this world's mystery before the game takes his life.
Both titles are shounen, battle oriented mangas about espers fighting each other. Both have a group of children, learning about their powers in special facility (though in ZKC they are main characters, while in Psyren they are only secondary cast).
Both mangas are centered around a prediction for the future disaster, caused by espers (espers raging a war on normals in ZKC, espers turning world into wasteland in Psyren). The good guys, try to stop that prediction from happening.
Generally if you like one, you should check the other as well.