In the current picture of nuclear astrophysics indirect methods and, in particular, the Trojan Horse Method cover a crucial role for the measurement of charged particle induced reactions cross sections of astrophysical interest, in the energy range required by the astrophysical scenarios. To better understand its cornerstones and its applications to physical cases many tests were performed to verify all its properties and the possible future perspectives. The key to the method is the quasi-free break-up and some of its properties will be investigated in the present work. In particular, the Trojan Horse nucleus invariance will be studied and previous studies will be extended to the cases of the binary d(d, p)t and 6Li(d,α)4He reactions, which were tested using different quasi-free break-up's, namely 6Li and 3He. The astrophysical S(E)-factor were then extracted with the Trojan Horse formalism applied to the two different break-up schemes and compared with direct data as well as with previous indirect investigations. The very good agreement confirms the independence of binary indirect cross section on the chosen spectator particle also for these reactions.