At the present time, physicians often treat patients with atrial fibrillation (AF) using radiofrequency (RF) catheter systems to ablate conducting tissue in the wall of the Left Atrium of the heart around the ostium of the pulmonary veins. These systems are expensive and take time consuming to use. The present invention circular ablation system CAS includes a multiplicity of expandable needles that can be expanded around a central axis and positioned to inject a fluid like ethanol to ablate conductive tissue in a ring around the ostium of a pulmonary vein quickly and without the need for expensive capital equipment. The expansion of the needles is accomplished by self-expanding or balloon expandable structures. The invention includes centering means so that the needles will be situated in a pattern surrounding the outside of the ostium of a vein. Also included are members that limit the distance of penetration of the needles into the wall of the left atrium. The present invention also has application to ablating tissue around the ostium of a renal artery for the treatment of hypertension.