Dynamical torsion gravity backgrounds

We write the field equations of torsion gravity theories and Noether identity they obey directly in terms metric contorsion tensor components expressed with respect to natural coordinates, i.e., without using vierbien but Lagrange multipliers. Then we obtain explicit solutions these equations, under specific ans\"atze for field, by assuming be respectively Bertotti-Robinson, pp-wave, Friedmann-Lema\^{\i}tre-Robertson-Walker or static spherically symmetric type. Among various some them have their depending on arbitrary functions that did not influence geometry. This raises questions about predictability theory.