Path follows shape object

Hi all

I get how an object follows a path; but i want my path in a screw around my object (which goes from thick to thin; so no ordinary tube.)
Anyone knows how to do this? Thx

Roughly position the path and use the shrinkwap modifier to shrink it onto the faces of your object.

Thanks, apparantly very simple. Thanks a lot!

One more tiny question: Do you perhaps know how i can randomize the size of the object that follows my path?