An electrosurgical probe comprises a shaft having an electrode array at its distal end and a connector at its proximal end. The array includes a plurality of isolated electrode terminals, and an electrosurgical power supply is provided with a multiplicity of independently limited or controlled current sources and a connector. The electrosurgical probe and the power supply may be connected through their respective connectors so that the independent current sources are connected to individual electrode terminals. In other configurations, the probe includes a single electrode terminal spaced from a return electrode such that when the electrode terminal is brought adjacent a tissue structure immersed in electrically conductive fluid, the electrically conductive fluid completes a conduction path between the electrode terminal and the return electrode. By applying very high frequency electrical energy to the electrode terminal, target tissue may be cut or ablated while heat dissipation through low impedance paths, such as blood and normal saline, will be minimized.