Single two-dimensional (2D) atomically thick magnetic particles of cobalt and iron with variable size and shape were fabricated by combining a mask technique with standard molecular beam epitaxy. Reduction of the Lateral size of in-plane magnetized 2D cobalt films down to about 100 nanometers did not essentially modify their magnetic properties; although the separation of boundaries decreased greatly, neither domain penetrated the particle, nor was any sizable shape anisotropy observed. The mutual interaction of 2D cobalt particles was negligible, and the magnetic state of a single particle could be switched without modifying the state of the neighbors. Perpendicularly magnetized iron particles did not exhibit such responses. These results suggest that only a few atoms forming a 2D in-plane magnetized dot may provide a stable elementary bit for nanorecording.