We quantify the rate of capture by Co islands on Ru(0001) of additionally deposited Cu atoms, using scanning tunneling microscopy. The dependence of the capture rates on Co-island size is shown to reflect larger island-free areas surrounding bigger islands, a feature neglected in mean-field treatments. We also find a strong direction dependence in Cu adatom capture, reflecting the local environment of individual islands. These features are elucidated by simulations and diffusion equation analyses.