We determine the relationship between the turnaround radius, Rt, and mass, Mt, in Λ CDM, 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 Λ CDM, and different dark energy models to that obtained in the f(R) modified gravity (MG) scenario. The Rt-Mt relationship in Λ CDM, 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.