Simply Put, I would have to say the APC. Anaphase Promoting complex. This is the single step which i believe causes cell division. It propagates all further activity. The role of the Anaphase Promoting Complex is to initiate Cohesin destruction. As you may or may not know, Cohesin is the very protein which keeps the sister chromatids together, when they are degraded, the two split apart, and the microtubules pull on each chromatid, causing the split. This is the step of telophase. There are many other regulators of this process, such as cdc25 (regulates the over-growth of the cell) and the wee1 complex (which allows the cell to split too soon).
Also reading the way that you voice your question, also makes me consider another process, which commits the cell to growth in late G1, and replication of a gene - Essentially the choice to divide is made quite early, and the choice to divide is perhaps what your looking for. Well when the cell is mature enough, or sees a need to divide. How does it do that?
''the cell “counts” the number of triggered IL2 receptors, and only decides to divide when the critical number has been attained. This information is then transferred to the cellular interior via intracellular sensors comprised of D-type cyclins, which ultimately determine when the cell surpasses the “Restriction Point” in late G1, and which commits the cell irrevocably to initiate DNA replication.''
This is actually a quote from one of my professors from UConn, but i think its pretty straight forward. There are many steps to cell division, and along the way there are what we like to call checkpoints. Hope its helpful.