First thoughts right after watching the Movie
My opinion right after watching the movie is that the transition of their friendship is very organic and natural, with it being one of the main redeemable and memorable qualities of the show.
Summary
Their first interaction is when Tadashi brings his brother to his school, and shows him his Baymax, who springs to life. Hiro is sarcastic, as he is speaking to Tadashi, while Baymax scans him, and tells Hiro all he knows about him, which causes Hiro to be impressed by the robot. The brothers talk about Baymax’s technological advancements, gadgets, etc. The robot cannot deactivate until Hiro says he is pleased with the service.
Baymax does not come to life again until weeks after Tadashi passes away, and activates when Hiro stumbles his toe due to a microbot. Hiro did not know that the robot is still active, and tells him he’s fine, but the teen continues to hurt himself, and the robot consoles him.

He finally catches up to the robot, and despite thinking earlier that it is broken, Hiro sees that it is moving to follow something. This leads the both of them to enter an abandoned building. Baymax gets on his nerves with being inefficient, and popping up randomly behind him, especially when the large amount of microbots chasing after them. At this point, it’s clear that Hiro is more annoyed than impressed with the robot, but there’s not enough there to claim dislike; just a slight irritant of his random antics.
While at the police office to make a report, Baymax’s battery runs low, with his behaviour representing one of a drunk and hungover person, who needs to be escorted back home. Baymax looks over to Tadashi’s hat, and repeats his name until Hiro tells him that Tadashi is dead. He claims that Tadashi was in good physical and mental health to live a long life, for Hiro to open up, and tell him that Tadashi died in a fire, and that he’s sick of the claim that “he’s always with us”. Baymax still does not get emotional reactions, so he downloads information from the internet about grief, and hugs Hiro, which he kind of reciprocates.

After Hiro opens up, there is literally no more hostility between the two of them, so whatever sort of “ice” or annoyance is gone. We have a montage scene where the team trains to be proper superheroes, and gain proper equipment. I have to bring up a point that is pretty important; Hiro is pretty much using and deceiving Baymax into doing all of this, not telling him everything that his plan consists of, claiming that it will make him feel better. Anyways, the two go on a nice flight across the town, and the robot realizes that it’s working, and Hiro is feeling better.
We get a scene where they all go after the masked man, and Hiro is more than pissed, so he tries to change Baymax’s program to destroy, and to destroy Krei, but Baymax is a bit iffy on this, claiming that it is not what Tadashi would have wanted. The teen snaps about Tadashi not being here anymore, and a video of over 80 attempts of Tadashi trying to get Baymax to work, and it cheers Hiro up, apologizing to Baymax.

We get to the epilogue, where Hiro is well-adjusted with the others in the team, and gives his aunt a hug before running off to school. He moves into a dorm room, and unpackages all of the boxes, where he gives the arm of Baymax a “props handshake” (which he taught Baymax earlier in the film). Within the fist is the healthcare chip that Tadashi created, and uses it to revive Baymax, and they end up hugging.
Final Thoughts
Well, it’s somewhat like a friendship, and kind of like a brotherly relationship as well, though there was some manipulation on Hiro’s part.