The terahertz (THz) band has attracted significant interest for future wireless networks. In this paper, a THz integrated sensing communications and powering (THz-ISCAP) system, where sensing is leveraged to enhance communications and powering, is studied. For a given total amount of time, we aim to determine an optimal time allocation for sensing to improve the efficiency of communications and powering, along with an optimal power splitting ratio to balance these two functionalities. This is achieved by maximizing between communications and powering either the achievable rate or harvested energy while ensuring a minimum requirement on the other. Numerical results indicate that the optimal system performance can be achieved by jointly optimizing the sensing time allocation and the power splitting ratio. Additionally, the results reveal the effects of various factors, such as THz frequencies and antenna aperture sizes, on the system performance. This study provides some interesting results to offer a new perspective for the research on THz-ISCAP.