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.
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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.
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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
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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.
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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.
movies.stackexchange.com/users/11099/Shougo Makishima
Roger Ebert mentioned in his review of  Léon: The Professional   But always at the back of my mind was the troubled thought that there  was something wrong about placing a 12-year-old character in the  middle of this action.   How would you describe the relation that developed between Mathilda and Leon in the movie?
How would you describe the relation between Mathilda and Léon?
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<character><leon-the-professional>
movies.stackexchange.com/questions/34196
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The relationship between Leon and Mathilda is rather complicated. Leon is hinted to be mentally challenged in some capacity and his only friend before Mathilda was his plant. The relationship between Leon and Mathilda is a rather complicated one, and is pretty much the cornerstone of the whole movie.   
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.