Hi Tobi,
Yes, at this point is difficult to make it (see my example blood_vessels_2.max). There you need to create an independent splines, and for each spline copy and configure a specific path. To start the path correctly, for each spline need to reorient pivot.
But we have plans to develop a Spline distributor, which would allow to start the path directly from the starting point of the splines. This will allow to solve your task much easier.
Cheers