closed as too broad by AliceD♦, fileunderwater, kmm, James, rg255 Oct 17 '16 at 20:50
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All eukaryotic cells have 'checkpoints' during their cell cycle (1)1. They will only commit to cell division or the next phase of mitosis until all requirements have been fulfilled. The cell needs to have enough energy and the right external stimuli before it starts the irreversible commitment to cell division. The proteins effecting these changes are the cyclins and the associated CDK's. These proteins integrate a wide array of signalling inputs (e.g. DNA duplication complete or no major DNA damage) and steer the proteins actually duplicating the DNA and the other machinery needed to split a cell. You can learn more about these proteins and their signals by googling 'restriction point'
If you interfere with cyclin D modifying proteins you can get very large or very small cells. One of the best understood proteins involved is WEE1 from fission yeast. If you knock this one out, you get very small cells (2).
In mammalian cells the size of the spindle during anaphase also seems to be crucial in splitting cells equally (although some divisions are asymetrical)(3).