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The history of ternary adders goes back to more than six decades ago. Since then, a multitude of ternary full adders (TFAs) have been presented in the literature. This paper conducts a review of TFAs so that one can be familiar with the utilized design methodologies and their prevalence. Moreover, despite numerous TFAs, almost none of them are in their simplest form. A large number of transistors could have been eliminated by considering a partial TFA instead of a complete one. According to our investigation, only 28.6% of the previous designs are partial TFAs. Also, they could have been simplified even further by assuming a partial TFA with an output carry voltage of 0V or VDD. This way, in a single-VDD design, voltage division inside the Carry generator part would have been eliminated and less power dissipated. As far as we have searched, there are only three partial TFAs with this favorable condition in the literature. Additionally, most of the simulation setups in the previous articles are not realistic enough. Therefore, the simulation results reported in these papers are neither comparable nor entirely valid. Therefore, we got motivated to conduct a survey, elaborate on this issue, and enhance some of the previous designs. Among 84 papers, 10 different TFAs (from 11 papers) are selected, simplified, and simulated in this paper. Simulation results by HSPICE and 32nm CNFET technology reveal that the simplified partial TFAs outperform their original versions in terms of delay, power, and transistor count.