Basil Karlo came up with the idea of starting the team when he was visited at the prison's hospital by Sondra Fuller, who was also known as "Clayface Four". Karlo noticed Fuller's powers and abilities and convinced her to gather the other Clayfaces to become an unstoppable force.
Following Karlo's master plan, Lady Clay impersonated Looker and manipulated people to break Clayface III out of Arkham Asylum. She also used these powers to mind control Clayface III and had him followed her command. Meanwhile, Karlo located the last remains of Matt Hagen, who was Clayface II, but despite his best efforts, Hagen could not be brought back to life.
The Mud Pack was finally formed of Karlo as the leader, Lady Clay as the second in command and Clayface III as an unwilling pawn. Once again, Karlo came up with a plan that would bring the downfall of Batman by sending Clayface III on criminal rampages alongside Lady Clay, who impersonated Batman to soil the vigilante's name.
Batman tried to stop them, but he fell into Karlo's trap and would've perished if the real Looker wouldn't have shown up to rescue him. Thinking that Batman was defeated, Karlo revealed his true intentions and double-crossed Lady Clay in order to steal a sample of her blood, as well as that of Clayface III. Karlo was the only Clayface with no real powers or abilities and so he used the other villains to steal their cells and become a real Clayface himself.
Karlo succeeded and became the Ultimate Clayface, gaining the powers of Lady Clay and Clayface III. The new transformation allowed Clayface to defeat Batman and Looker combined, until Looker overloaded his system and Clayface's corrosive touch caused him to burn his way through several feet below ground. Without a leader, the Mud Pack was officially disbanded and after learning about Karlo's manipulation, Lady Clay and Clayface III started a romantic relationship outside of Gotham City.
Links and References