I will discuss scale-free Einstein equations, introduced in e-Print: 2011.07055. In these equations the trace part is lost in a way different from the one in unimodular gravity. These equations are classically equivalent to General Relativity, yet the Newton constant becomes a constant of integration or a global dynamical degree of freedom. Thus, from the point of view of standard quantization, this effective Newton constant is susceptible to quantum fluctuations. This is similar to what happens to the cosmological constant in unimodular gravity. Using analogy with the Henneaux-Teitelboim covariant action for unimodular gravity, we consider different general-covariant actions resulting in these dynamics. This setup allows one to formulate the Heisenberg uncertainty relations for the Newton constant and canonically conjugated quantities. Interestingly, a quasiclassical description in these global theories requires a minimal level of quantum fluctuations of the Newton constant in the same way as cosmological constant has a minimal level of quantum fluctuations in the unimodular gravity, see e-Print: 2107.09601. Unexpectedly, one of such theories also promotes Planck's quantum constant to a global degree of freedom, which is subject to quantum fluctuations. Following analogy with the unimodular gravity, we discuss non-covariant "unimatter" and "unicurvature" gravities describing the scale-free Einstein equations. Finally, we show that in some limit of the Yang-Mills gauge theory a "frozen" axion-like field can emulate not only the cosmological constant, but also the gravitational Newton constant or even of the quantum Planck constant.