Origin

Zook was the silver-age side-kick, and/or pet of the Martian Manhunter. He arrived on Earth when a space warp opened from another dimension and two criminals arrive pursued by R'ell, a law enforcement officer from that universe. By accident another creature, a different species from the first 3 follows them through. This was Zook.

R’ell says the creature is one of the Zooks, and nothing but a mischievous animal, and indeed Zook does then proceed to make the capture of the two criminals more difficult. In the end during the battle with the criminals, J'onzz is able to grab all three of them up and toss them though the space warp just before is closes. It is then that he finds he has forgotten about the fourth creature.

Before long the "mischievous animal" learns to speak a simple form of English, and demonstrated that he has an array of unusual abilities, which he uses to help the Martian Manhunter on his cases, including Temperature Manipulation, shape-changing/stretching, and tracking; Zook can even identify Manhunter when he has taken other forms.

Post Crisis, the adventures including Zook were no longer canon, and in the 1998 Martian Manhunter series a plant native to old Mars is called a Zo'ok; it is worn by J'onn J'onzz as a shape-shifting costume. This was not referred to outside of that series, and Zook would appear again, post Infinite Crisis in the Superman/Batman storyline The Enemies Among Us.

Other Media

Supergirl

While he doesn't appear, he's mentioned to be an imaginary friend of Martian Manhunter. Although it was confirmed by writer Eric Carrasco that Zook was real, and an imp that would visit J'onn as a kid, this was to have Zook appear later on the show but the series ended before that plot point would be resolved.