l-adic points on Modular Towers

In the opposite direction, using Harbater patching method we can construct projective systems of points on the Hurwitz modular tower defined over the maximal unramified extension Q, l of Q_{l and lying on coherent systems of g-p,-components. The question whether the same is possible on other type of components-an a rmative answer to this question is more or less equivalent to the negation of the "Harbater patching converse"-is still open to my knowledge. In this direction we'll give an example of points defined over Q, l on non g-p,-components of arbitrary high level in the modular tower relative to the universal Frattini cover of the dihedral group Dp. But they don't form a coherent system of points.}