Fill area behind animated line I'm animating lines.
Similar to this:  (Let text follow animated beziercurve) 

Now I would like to fill in the area behind the curve.
Similar to this:



so that if I move my line than the filled area also moves.
(It would be ideal if there is a gradient that the color is stronger near the line and fades out to transparent when further away.).

any suggestions on how to start this?
if I got what you mean, you could toggle cyclic (ALT-C) on the 2D curve in edit mode, to get a fill. In Blender there's no concept of "object border" but you could use freestyle to obtain something usable maybe. 

Here is the overall setup from which you could start...



for the fill, you should be able to use a "Blend" texture type using also transparency, see second image example