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, and the two were 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. When Zane regained this memory, he was sad to recall his father's death, but shed a tear with a smile.
In Season 2, they are reunited when it is revealed that Dr. Julien was resurrected by Samukai, and had been imprisoned ever since on an island. Dr. Julien revealed that he wanted to see Zane again, explaining that Samukai used that fact as leverage against him. Zane and the Ninja liberated Dr. Julien, and he and Zane promised to spend time together now that fate had given 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 creates an ice statue of Dr. Julien to pay his respects to his father, but becomes sad and angry when the ghost of Cryptor destroys it.
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 them. 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 having found someone so special to him. When Zane sacrificed himself, P.I.X.A.L. was the one who took his death notably hard, to the point where she didn't attend his funeral. Because of this, she would be the first person to see him reconstruct himself in a new updated body, and smiled greatly when he revealed his presence to her in the Borg Industries computers by asking if they were compatible.
In Season 4, the two were captured and brought to Chen, who held them prisoner on his secluded island to draw out the other Ninja. In the early stages of his imprisonment, Zane was amnesiac, and it was P.I.X.A.L. who guided him back to his memories. The return of his memory is signaled by Zane asking P.I.X.A.L. if they are compatible, which she affirms. When Zane broke out, he was disheartened to learn that P.I.X.A.L had been dismantled. Despite P.I.X.A.L.'s urging to leave without her, he refused to abandon her, placing her memory card into his own system and allowing her to continue the journey with him—audible only as a voice inside his head, and visible in his field of vision as a small image on a screen. 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 came face to face with Nadakhan, P.I.X.A.L. tried to warn him of the consequence, but he ignored her warning. He came to regret his choice when Nadakhan removed her from his processor, which left him distraught 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 her input in later adventures.
In Hands of Time, when an attack by Acronix put Zane offline, P.I.X.A.L. expresses worry, and tries to wake him. 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 one of Wu's students, along with the other Ninja. When Zane and the others trained to become Ninja, they were shown to really cared about Wu and are glad to have Wu as their master. When Zane is socially outcast at the beginning of the Ninjas' training all together, Wu encourages the other Ninja to look at Zane as a brother, asking them, "What is 'weird?'" Like the other Ninja, Zane respects 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.
In Season 8: Sons of Garmadon, it is revealed that the two already met and Wu told Zane that he might call upon for something in the near future. Zane couldn't recall this as Julien wiped his memory before his first death.
Like the others, Kai thought Zane was odd, but grew to care for and defend him even if he didn't totally understand him. When he learned that Zane was a Nindroid, he and the others supported and accepted their friend. When Zane sacrificed himself to defeat the Digital Overlord, Kai was the one shown delivering his eulogy.
In Season 4, Kai and the others protested Lloyd's idea of replacing Zane on the team, even 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 to comfort him 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 complained that Zane was weird at first. But when he found 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, to the point that Wu needed to hold Jay back from running after him.
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 at first by Zane's personality, but grew to be his friend like all the rest. When he found out Zane was a Nindroid, he was the first to offer comfort, stating that he's still the same Zane, he's "just got more . . . gears" and later affectionately nicknaming him "Tin Can."
In Season 4, Cole and the others were adamant about not replacing Zane on the team, but that argument was cut short when they spotted a poster that claimed he was still alive, prompting them to enter Chen's fighting tournament to find him. Cole was the first to find Zane, and they immediately worked together and broke free, reuniting with a hug. But due to Cole's promise of breaking the other Elemental Masters out of Chen's grasp, he implored Zane to leave while he went back. To his surprise, Zane decided to help him, telling Cole that Ninja never leave one another behind. After a series of plans, they were successful in liberating the captives and joined their allies in defeating Chen.
In "Day of the Departed," Zane and the others were very happy that Cole was fine and became a human again.
Lloyd and Zane are good friends throughout the series, with Zane initially acting as a mentor, then more and more as an equal friend. Lloyd and the other Ninja really missed Zane after he sacrificed himself to defeat the Overlord. In season 4, Lloyd worked hard to help the other Ninja move on, and suggested finding a new addition to the team, but 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, Zane telling him 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 was sad about Zane's apparent death, but, when searching for the other Ninja, was surprised to detect Zane's recon beacon. When she found the Ninja on Chen's Island, she immediately ran 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 was attacked by Krux and Acronix, she worked very hard to restore him after he spent a while unconscious. Nya was successful in awakening Zane, and was relieved to have him back in action.