The mechanism by which spindle microtubules (MTs) determine the site of cell division in animal cells is still highly controversial. Putative cytokinesis "signals" have been proposed to be positioned by spindle MTs at equatorial cortical regions to increase cortical contractility and/or at polar regions to decrease contractility [Rappaport, 1986; von Dassow, 2009]. Given the relative paucity of MTs at the future division site, it has not been clear how MTs localize cytokinesis factors there. Here, we test cytokinesis models using computational and experimental approaches. We present a simple lattice-based model in which signal-kinesin complexes move by transient plus-end directed movements on MTs interspersed with occasions of uniform diffusion in the cytoplasm. In simulations, complexes distribute themselves initially at the spindle midzone and then move on astral MTs to accumulate with time at the equatorial cortex. Simulations accurately predict cleavage patterns of cells with different geometries and MT arrangements and elucidate several experimental observations that have defied easy explanation by previous models. We verify this model with experiments on indented sea urchin zygotes showing that cells often divide perpendicular to the spindle at sites distinct from the indentations. These studies support an equatorial stimulation model and provide a simple mechanism explaining how cytokinesis factors localize to the future division site.