In this paper, we study the fundamental limits of simultaneous information and power transfer over a Rayleigh fading channel, where the channel input is constrained to peak-power constraints that vary in each channel use by taking into account high-power amplifier nonlinearities. In particular, a three-party communication system is considered, where a transmitter aims simultaneously conveying information to an information receiver and delivering energy to an energy harvesting receiver. For the special case of static PP constraints, we study the information-energy capacity region and the associated input distribution under: average-power and PP constraints at the transmitter, an HPA nonlinearity at the transmitter, and nonlinearity of the energy harvesting circuit at the energy receiver. By extending Smith \' mathematical framework, we show that the optimal input distribution under those constraints is discrete with a finite number of mass points. We show that HPA significantly reduces the information energy capacity region. In addition, we derive a closed\-form expression of the capacity achieving distribution for the low PP regime, where there is no trade-off between information and energy transfer. For the case with time-varying PP constraints, we prove that the optimal input distribution has a finite support by using Shannon\'s coding scheme. Specifically, we numerically study a particular scenario for the time-varying PP constraints, where the PP constraint probabilistically is either zero or equal to a non-zero constant.