In the movie, Tadashi spends a lot of time and effort to create Baymax, and it was hinted that it was even taxing on the young man's health and patience. However, Tadashi never gave up, and after 84 trials, he finally gets the robot working properly, and is overjoyed. Baymax, with his robotic brain, seems to value Tadashi as his creator, even asking where he had gone (and when he would return) before finding out that Tadashi had been killed in a fire. In an interview, Baymax mentions that one of the reasons he values Hiro so much is because Hiro is Tadashi's brother.
The dynamic of robot/inventor is the most common one that fans like to use in the fandom. (Maybe even extending to a sort of father/son relationship, as Baymax is Tadashi's brainchild.) The two of them are often seen with Hiro--and sometimes with Aunt Cass and Mochi --as a big family. A romantic interpretation between Tadashi and Baymax is rare, but there are some fans who enjoy it.
In the movie, when Tadashi dies, Hiro sees Baymax as the last remaining shred of his brother and allows the robot to fill the void in his heart. Many fan interpretations say that Tadashi's spirit is watching over Hiro through Baymax, some even going so far to say that Tadashi literally resides within Baymax and may even control his actions (in some of the more comedic fanwork, Tadashi is seen to be physically stuffed inside of Baymax, though this isn't a fan interpretation as much as it is an inside joke between the fans). In an AU where Tadashi doesn't die, this isn't the case, but Baymax is still very important in the lives of both Tadashi and Hiro.
Note: Please only add examples that are part of the RotBTD fandom.