The growth of uniform nanostructures requires simple and reproducible ways to control the size. It is found that Co atoms can form two-dimensional structural islands on √3 x √3-Ag/Ge(111) surfaces. Temperature and Co coverage are two factors to modulate the island size. By using scanning tunneling microscopy, the surface structures and morphology for different annealing temperatures and variable Co coverage have been investigated. For 100 degrees C annealing temperature, Co atoms are difficult to condense into structural islands at 0.35 ML whereas several structural Co islands are found at 1.4 ML. This difference is due to the quantity of Co atoms per unit area for forming structural islands. As the temperature increases, Co atoms get more energy to diffuse. Therefore, the average island size increases with rising temperatures until the coverage of 3.5 ML. Yet, the island size stops growing above the coverage of 3.5 ML because of the limitation for the Co covered area. Therefore the Co islands increase their height rather than their size. In addition, the shape of Co islands can also be controlled. It transforms from random shapes to the hexagonal shape with increasing temperature.