As Internet of Things (IoT) devices proliferate, sustainable methods for powering them are becoming indispensable. The wireless provision of power enables battery-free operation and is crucial for complying with weight and size restrictions. For the energy harvesting (EH) components of these devices to be small, a high operating frequency is necessary. In conjunction with a large transmit antenna, the receivers may be located in the radiating near-field (Fresnel) region, e.g., in indoor scenarios. In this paper, we propose a wireless power transfer (WPT) system ensuring reliable supply of power to an arbitrary number of mobile, low-power, and single-antenna receivers, whose locations in a three-dimensional cuboid room are unknown. A max-min optimisation problem is formulated to determine the optimal transmit power distribution. We rigorously prove that the optimal transmit power distribution's support has a lower dimensionality than its domain and thus, the employment of a continuous aperture antenna, utilised in Holographic MIMO (HMIMO), is unnecessary in the context of the considered WPT problem. Indeed, deploying a discrete transmit antenna architecture, i.e., a transmit antenna array, is sufficient and our proposed solution provides the optimal transmit antenna deployment and power allocation. Moreover, for a one-dimensional transmit antenna architecture, a finite number of transmit antennas is proven to be optimal. The proposed optimal solution is validated through computer simulations. Our simulation results indicate that the optimal transmit antenna architecture requires a finite number of transmit antennas and depends on the geometry of the environment and the dimensionality of the transmit antenna array.