How would you describe the relation between Mathilda and Léon?

The relationship between Leon and Mathilda is a rather complicated one, and is pretty much the cornerstone of the whole movie.

Leon is hinted to be mentally challenged in some capacity. He can't read and despite his prowess as an assassin is very naive and is easily fooled by Tony (and Mathilda). He also has problems with intimacy and letting people get close to him. His only real friend before Mathilda was his plant. At first he struggled a lot with allowing Mathilda to enter his life, going as far as attempting to kill her while she slept. Soon enough, Mathilda becomes his friend and a surrogate daughter figure.

Mathilda on the other hand is smart and savvy beyond her years. She comes from a dysfunctional home where she is despised by everyone. She too has no real friends. She's go starved for human contact that Leon's passing attempt at small talk immediately makes her latch on to him and offer to get him his groceries. Eventually, as her relationship with Leon progresses, she finds herself falling in love with him. Leon (and the audience) are left to ponder if it's true attraction or just an infatuation with the only adult-figure who has been kind to her.

The two broken human beings flock together and form a family-unit of sort. To an audience used to normal families, a very young girl with a crush on a mentally and emotionally challenged hitman is very uncomfortable. In fact, American test audiences were so uncomfortable that a scene where Mathilda (unsuccessfully) propositions Leon to sleep with her was cut for the American release. One could argue that this discomfort is an intentional part of the movie.

Despite the guns and knives and bombs and drugs, the relationship is innocent. Leon is essentially a child in a man's body, he cannot read, Tony is his surrogate father taking care of him financially and he and maltilda play "dress up".

In this relationship he learns for the first time about love and he develops into matilda's surrogate parent.

In the original draft, Mathilda (aged 13 or 14) and Léon become lovers. Besson reportedly altered the script to remove this aspect of the story (possibly due to pressure from Portman's parents). The initial cut of the film had more scenes with "awkward sexual tension" between Mathilda and Léon. These scenes were later removed for the American release, dubbed The Professional, but were included in the 1996 European release, as well as in the deleted scenes of the special edition DVD. They were reintegrated back into the film for the "International Cut," which is now available on Blu-ray/DVD. When the film was first tested in Los Angeles, the movie included a short scene where Mathilda asks Léon to be her lover. However, the audience became extremely uncomfortable and began to laugh nervously, completely destroying the tone of the film. Because of this, the movie received terrible test scores and Besson and producer Patrice Ledoux decided to cut the scene for the American theatrical release.

http://www.zimbio.com/Beyond+the+Box+Office/articles/UeZ2d6FD2ub/20+Things+May+Not+Know+L+Professional

Younger and the relationship would either have to be totally creepy or transform into more obviously paternal relationship. Older, say 16+, and the relationship likely is forced to take on more romantically charged aspects. At 12-14, the character can be old enough to be somewhat independent and for the relationship to be a friendship rather than paternal and young enough for it to avoid romantic questions.

Definitely romantic (controversial scene):

Mathilda: Leon, I think I'm kinda falling in love with you.
[Leon chokes on his milk]
Mathilda: It's the first time for me, you know?
Léon: [wiping himself off] How do you know it's love if you've never been in love before?
Mathilda: 'Cause I feel it.
Léon: Where?
Mathilda: [stoking her stomach] In my stomach. It's all warm. I always had a knot there and now... it's gone.
Léon: Mathilda, I'm glad you don't have a stomach ache any more. I don't think it means anything.

Director Luc Besson didn’t intend for anyone to think Léon had a sexual interest in Mathilda. She tries to seduce him and thinks she’s in love with him, but it’s important to remember she’s a child. She doesn’t know what her emotions mean - she’s merely in a situation where she’s finally allowed to have them. Her family life was terrible, she witnessed her family’s murder, and Léon is the first person who genuinely cared for her. He’s a paternal figure, a protector, and the only man in Mathilda’s life. The only person she ever truly cared about was her little brother, who was murdered with the rest of her family. She transfers her love for him, and her longing for the father she never had, onto Léon. She’s 12 years old and on the edge of puberty - it’s completely reasonable for her to not know how to handle all these various emotions.

Léon himself is a bit of a child in the ways that Mathilda isn’t. He drinks milk a lot and can’t read. Aside from being an assassin, he’s very reserved, naive, and disconnected. His feelings toward Mathilda awaken an appreciation for life and show there’s a reason for him to exist. But he never responds with even the slightest glimmer of interest in her emotional advances. He loves her, but not romantically. Jean Reno does an excellent job conveying his discomfort every time Mathilda attempts to act beyond her age or understanding. He’s an assassin, and could easily be an immoral character more than willing to take advantage of a 12 year-old throwing herself at him, but he does the exact opposite.