Gaz does seem not care about Zim or fear him due to him being stupid to try to take over the Earth but this could be due to her lack of interaction with him. So far, the only episode with elongated interaction between Zim and Gaz is "Bloaty's Pizza Hog" where Gaz is forced to rescue her brother from Zim, but only for the reason of a family night out.
So far Gaz will have a little interaction with Zim. In the unaired episode "Ten Minutes Of Doom", Gaz will unknowingly retrieve Zim's PAK from Dib.
In this unfinished unplot last episode/film, which takes place 10 years after the series, Gaz would have secretly joined Zim to help him fight against her brother Dib, Tak, The Resisty, and The Meekrob, who are planning to not only to eliminate Zim but the entire Irken race,the planet and probably Earth as well (due to Dib being bullied and ignored by his own kind). She would have disguised herself by wearing a black or brown cloak showing only her beautiful hazel eyes and during their time together both would had started showing feelings for one another (This was confirmed by Jhonen Vasquez, creator of the show). As the war ended, Zim and his crew would have saved the Irken race and Earth; Gaz would've then revealed her true identity to Zim, who becomes the new Almighty Tallest.
Zim then banished Dib, Tak, and their crew to Saturn and banishing the Red and Purple as well. Zim makes Gaz into his new empress/wife for helping him and both would rule Irk together.
- In the InvaderCon II 2012, Jhonen claimed that had he put romance in the show, he would've paired Zim and Gaz.
- Fans have named this relationship the ZAGR, which stands for Zim And Gaz Romance.
- Both voice actor and actress of Zim and Gaz had approved of this relationship.
- Jhonen Vasquez hates both ZADR (Zim And Dib Romance) and ZATR (Zim And Tak Romance) as he claims to his fans they will always be enemies but he leaves the door open for Zim & Gaz.
- Jhonen Vasquez approves Zim and Gaz Romance.
- In the unplot film, Gaz would be 21 years old as legal age (As confirmed by Jhonen Vasquez himself) so she can be with Zim due to him being way more older than her and, due to lower gravity on Earth, Zim becomes taller than Gaz (and even passes the height of The Almighty Tallest, Red and Purple).
- Zim and Gaz relationship is compared to another relationship, Johnny and Devi in Jhonen's comic book series, Johnny The Homicidal Maniac.
- Like all Nickelodeon's lead cartoon characters who have kids of his or her own, it's unknown if Zim and Gaz will have kids together.
- Gaz is a playable character in Nicktoons: MLB alongside Zim, with surprisingly positive interaction with him. When ZIM passes first base during a home run, Gaz can briefly be seen cheering for him when he passes her during it.