Planetary gear trains (PGT) are widely used in automatic transmissions (AT), hybrid electric powertrains (HEP) and plug-in hybrid electrical powertrains (PHEP) for automotive vehicles. Many PGTs have been developed by the industry including 6, 7, 8, 9 or 10 speeds automatic transmissions for internal combustion engine (ICE) powertrain systems; PGTs with two electrical machines (EM) and an ICE for single mode or multi-mode HEP systems; PGTs with single EM and an ICE for PHEP systems. Facing the new competitive challenges in motor vehicle electrification, synthesizing the simpler or if possible simplest PGTs for PHEP becomes an important task. The work reported in this article is such an effort which results in much simpler, if not the simplest, PGT designs for PHEP as well as for automatic transmissions. For example, with three planetary gear sets and five clutches, the work achieved all the following features with one integrated PGT design: seven gear ratios for ICE drive, four gear ratios for electrical machine (EM) drive, and a generator-assisted ICE vehicle launch operating mode which provides smooth vehicle launch operation without a traditional launch device (torque converter or launch clutch) when the electrical battery is depleted. Similarly, with four planetary gear sets and five clutches the following features are achieved: nine gear ratios for ICE drive, four gear ratios for EM drive, and generator-assisted ICE vehicle launch modes. With two planetary gear sets and five clutches the following feature are achieved: four gear ratios for ICE drive, four gear ratios for EM drive, and generator-assisted ICE vehicle launch modes. The design methodology and the details of the results will be reported.