Max is very bright, and has an interest in cleaning and science – notably astronomy and oceanography. Not to mention, he also likes watermelon Jolly Ranchers. He is seen watching a live satellite feed of Pluto, lists oceanography as an interest, and refers to his love of Discovery Channel's "Shark Week." He is learning to play the trombone, but does not appear to have been playing for very long. Like his mother, Max loves animals, and the family dog (which he names Cosmo T.D. Fuller) is technically his, having been promised a dog after his goldfish died. Max mentions that he likes looking "snazzy" (stylish) in "The Not-So-Great Escape", and displays nearly the same level of enthusiasm for cleanliness that his grandfather, Danny does. Max shares a room with Jackson (similar to when D.J. shared a room with Stephanie. D.J. eventually moved into Michelle's room and Stephanie shared a room with Michelle until the end of Full House). Max has also been known to be a "neat freak", much like his grandfather, Danny.
Max looks up to his big brother Jackson. Max was thrilled with the idea of sharing a room with Jackson. Like Jackson, Max enjoys Mexican Wrestling.
- D.J. Tanner-Fuller (mother)
- Tommy Fuller, Sr. (father) (deceased)
- Jackson Fuller (older Brother)
- Tommy Fuller, Jr. (younger Brother)
- Danny Tanner (grandfather)
- Pamela Tanner (grandmother) (deceased)
- Teri Tanner (step grandmother)
- Stephanie Tanner (aunt)
- Michelle Tanner (aunt)
- Claire Tanner (great-grandmother)
- Wendy Tanner (great-aunt)
- Jesse Katsopolis (great-uncle)
- Rebecca Katsopolis (great-aunt)
- Nicky Katsopolis (first cousin, once removed)
- Alex Katsopolis (first cousin, once removed)
- Nick Katsopolis (great-grandfather)
- Irene Katsopolis (great-grandmother)
- In "Mad Max", it is revealed that Max attends Harvey Milk Elementary School, unlike D.J., Stephanie, Michelle, Kimmy, and presumably Nicky and Alex who attended Frasier Street Elementary School as children.
- Max is right-handed.
- He has been known to be smart for his age.
- "Holy chalupas!"
- "Well, well, well..."
- "I'm the king of the world!"