Almost found the solution... You were right about the use of success: fadeOutResponse. I had tried success: fadeOutResponse() and believe it or not it doesn't produce the same result ! I don't know why but when I use success: fadeOutResponse() the function is executed as soon as I load the page. (Without the () it works and the function is executed when the form is submitted succesfully). BUT this means that I cannot make this fadeOutResponse function work for any div I would like to hide. fadeOutResponse(#anyelement) is executed when the page is loaded.
I would obviously like to avoid having one function per div I have to hide so do you think there is a solution ? Thanks.