These are the relationships of the Titanium Ninja, Zane.
Dr. Julien is Zane's creator and father. He built Zane years ago and treated him no differently from a human son, with the two being happy in the time they spent together. When Dr. Julien was about to die, he erased Zane's memory to spare him the pain of his loss, but Zane soon regained this memory and was sad to recall his father's death.
In Season 2, they are reunited when it is revealed that Dr. Julien was resurrected by Samukai. Dr. Julien reveals that he wanted to see Zane again, explaining that Samukai used that as leverage against him. Zane and the Ninja liberated Dr. Julien, and he and Zane promised to spend time together now that fate gave them the chance. Dr. Julien became an ally of the Ninja and spent more time with his son, who was happy with his presence.
In Season 3, it is revealed that Dr. Julien passed away again when Cyrus Borg gives Zane his condolences and Zane accepts them. On the "Day of the Departed," Zane created an ice statue of Dr. Julien to pay his respects to his father, but became sad and angry when the ghost of Cryptor destroyed it.
The previous Elemental Master of Ice is Zane's ancestor, who previously held the power of Ice.
It is currently unknown how Zane had inherited the element of Ice, since he is a Nindroid, and how his predecessor is connected to him gaining the power.
Zane first encountered P.I.X.A.L. when he and the other Ninja arrived Cyrus Borg's building and he felt an attraction towards her as she was confused by his functioning. During the conflict with The Overlord, P.I.X.A.L. would be given some of Zane's power source to save her and would begin to feel human emotions with both saying the other was vital to the other. Indeed, they would come to the other's aid on many occasions after the Cryptor and the Nindroids attack. Their attraction was noted by a few characters such as Edna, Nya, and Kai, who all express happiness at Zane for finding someone special to him. When Zane sacrificed himself, P.I.X.A.L. was the one who took his death much harder to the point where she didn't attend his funeral. However, she would be the first person to see him reconstruct himself in a new body and smile at his question if they were compatible.
In Season 4, the two are captured and brought to Chen, who holds them there to draw out the other Ninja. In the early stages of his imprisonment, Zane is amnesiac and it is P.I.X.A.L. who guides him back to his memories, which helps him when he asks if they were compatible, to which she confirms. When Zane broke out, he was dishearten to learn that P.I.X.A.L had been dismantled as she encouraged him to go on without her but he refused to abandoned her and placed her memory card into his own programming allowing her to continue the journey with him acting as an advisor. It was P.I.X.A.L. who helped Zane in conquering his fears and unlocking his dragon.
P.I.X.A.L. would continue offering aid to Zane in his later fights such as with Morro. During Skybound, when Zane comes face to face with Nadakhan, P.I.X.A.L. tried to warn him of the consequence but he ignored her warning. However, he came to regret his choice when Nadakhan remove her processing which left him sad at the thought of living without her and forced him to make his last wish for it to go away. Due to Jay's last wish, Zane was reunited with P.I.X.A.L. and would continue to ask for input in later adventures.
In Hands of Time, due to an attack by Acronix, Zane was put offline to her worry and she tried to get him to awake. When Zane was reactivated by Nya, he was confused by P.I.X.A.L not responding to him and became sad as he realized he was alone.
Zane is Wu student, along with the other Ninja. When Zane and the others trained to become Ninja, they showed to really cared about Wu and are glad to have Wu as their master. Like the other Ninja, Zane respect Wu, who in turn views Zane and the others as his greatest students. In Season 4, when Zane was restored Wu was relieved to see him alive again and complimented his new form after reuniting with him.
Like the others, he thought Zane was odd, but when he find that Zane was a Nindroid, he and the others supported and accepted their friend. In Season 4, Kai and the others even protested against the decision to replace Zane when he was seemingly destroyed. He was willingly going to risk himself in the Tournament of Elements to find him. After reuniting with Zane, Kai was relieved to see him alive and well before the two worked together to defeat Chen and his forces. In Skybound, Zane placed his hand on Kai's shoulder after Nya was struck with a dart of Tiger Widow venom and succumbed to the effects of the poison.
Like all the other Ninja he thought Zane was weird but when finding out that Zane was Nindroid, he and the others supported and accepted their friend. They grew close through the series with Jay being devastated by Zane's sacrifice to defeat The Overlord.
In Season 4, Jay protested Lloyd's decision to replace Zane but when he learned that Zane was alive, he set out with the others to locate him. While imprisoned by Chen, Jay was reunited with Zane being elated to see his friend again and complimented his new form. Jay later marveled at Zane's ability to summon an Elemental Dragon, inspiring him to do so himself.
Like the others, Cole was put off by Zane's personality but when finding out he was Nindroid, they supported and accepted their friend. In Season 4, Cole and the others were adamant about not replacing Zane until they spotted a poster that said he was still alive, causing them to enter Chen's fighting tournament to find him. Cole was the first to find Zane and immediately worked together to break him and the other Elemental Masters out of Chen's grasps.
Lloyd and Zane are good friends throughout the series. Lloyd and the other Ninja really missed Zane after he sacrificed himself to defeat The Overlord. In season 4, though Lloyd attempted to move on and find a new addition to the team, he stopped when the Ninja discovered Zane was alive and set out to find him. While dueling Chen's forces, Lloyd was happy that they finally rescued their friend as Zane stated it was good to be back. After Chen launched his invasion, Lloyd used the loss of Zane as motivation to keep strong and as a sign that everything would be alright.
Nya and Zane get along very well and are friends throughout the series. In Season 4, Nya is sad about Zane's "death" but when searching for the other Ninja, she is surprised that she detected Zane's recon beacon. When she finds the Ninja on Chen's Island, she immediately runs to hug the newly rebuilt Zane relieved that he was back.
In Season 6, when Nya was struck with Tiger Widow venom, Zane was sad at her death but, fortunately, these events were undone due to Jay's last wish.
In Season 7, when Zane is attacked by Krux and Acronix, she works very hard to restore him after he is unconscious for a while. Nya was successful in awakening Zane and was relieved to have him back in action.