We point out that the ability of some models of inflation, such as the Higgs inflation and the universal attractor models at large values of the coupling ξ, in reproducing the available data is due to their relation to the Starobinsky model of inflation. For large field values, where the inflationary phase takes place, all of these classes of models are indeed identical to the Starobinsky model. Nevertheless, the inflation is just an auxiliary field in the Jordan frame of the Starobinsky model, and this leads to two important consequences: first, the inflationary predictions of the Starobinsky model and its descendants are slightly different (albeit not measurably); second, the theories have different small-field behavior, leading to different ultraviolet cutoff scales. In particular, one interesting descendant of the Starobinsky model is the nonminimally coupled quadratic chaotic inflation. Although the standard quadratic chaotic inflation is ruled out by the recent Planck data, its nonminimally coupled version is in agreement with observational data and valid up to Planckian scales.