We determine the relationship between the turnaround radius, Rt, and mass, Mt, in ΛCDM, and in dark energy scenarios, using an extended spherical collapse model taking into account the effects of shear and vorticity. We find a more general formula than that usually described in literature, showing a dependence of Rt from shear, and vorticity. The Rt-Mt relation differs from that obtained not taking into account shear, and rotation, especially at galactic scales, differing ≃30% from the result given in literature. This has effects on the constraint of the w parameter of the equation of state. We compare the Rt-Mt relationship obtained for the ΛCDM, and different dark energy models to that obtained in the f(R) modified gravity (MG) scenario. The Rt-Mt relationship in ΛCDM, and dark energy scenarios are tantamount to the prediction of the f(R) theories. Then, the Rt-Mt relationship is not a good probe to test gravity theories beyond Einstein's general relativity. Copyright © 2020 American Physical Society.