Programatically detect which list is used in the form

I'm creating a web part to be added on a form (DispForm, EditForm, NewForm) that will control the visibility of the form's fields.

On the web part's tool part, I'm planning on displaying the list of fields available for them to toggle visibility on.

I'd like to do this without having to require them to select what the list is. I'd rather have it determined dynamically if possible.

So is it possible then to do this: programatically determine the list used on a form page?