TGD predicts (see this , this , and this) a fractal network of very massive long cosmic strings which can locally thicken to flux tubes: this thickening involves transformation of dark energy and possible dark matter of cosmic string to ordinary matter giving rise to galaxies and other structures. Also stars would have thickened flux tube tangles insidde themselves. The model finds supports from the observation that galaxies form long strings as found decades ago (Zeldowich was one of the discoverers).
The TGD based model predicts the formation of planes in which objects in various scales move. The prediction is fractal: this applies to planets around stars, stars around galaxies, satellite galaxies arond larger galaxies,....
This model explains the newest anomaly and also the earlier anomalies if the galaxies are associated with the long "cosmic strings" predicted by TGD. They create a strong gravitational potential giving rise to a radial force in the plane orthogonal to the cosmic string. The motion along the string is free whereas the planar motion is rotation. The velocity spectrum is flat as required by the flatness of the galactic velocity spectrum. In the simplest model cosmic string is the carrier of galactic dark matter and dark energy. No dark matter halo and no exotic dark matter particles are needed.
Helical orbits are the most general orbits. If a concentration of matter occurs to a plane, it tends to catch objects moving freely in the direction of string to its vertical gravitational field and planar sheets such planetary systems, spiral galaxies, and the planar systems formed by satellite galaxies can form.
One can of course wonder whether there is something which serves as a seed for the concentration around particular plane. In TGD, space-time is a 4-surface in H=M4×CP2 and also membrane like entities are predicted as 4-D minimal surfaces in H. For instance, objects M1×X2×S1 are predicted, where M1 is time axis, X2 is a piece of plane of E2, and S1 is a geodesic sphere of CP2. Universe would be populated by these membrane-like objects. Cell membrane is one important example. These approximately planar objects orthogonal to the cosmic string could tend to gather the matter flowing along helical orbits along the cosmic string. These planes would accompany planetary, galactic, etc... planes.
Warped planes represent slightly more complex solutions (a thin metal foil or sheet of paper gets warped) for which the plane is deformed but still flat minimal surface. I am not sure whether the "warping" of the outer regions of galactic planes, which has received attention recently (see this and this) but has been detected already 1956, is really really warping that is vertical deformation, which depends only single coordinate varying along a straight line (2-D plane wave of membrane).
See the article Cosmic string model for the formation of galaxies and stars or the chapter with the same title.
For a summary of earlier postings see Latest progress in TGD.