What is the highest possible replication rate for living organisms? The cellular growth rate is controlled by a variety of processes. Therefore, it is unclear which metabolic process or group of processes should be activated to increase growth rate. An organism that is already growing fast may already have optimized through evolution all processes that could be optimized readily, but may be confronted with a more generic limitation. Here we introduce a method called 'cell selection' to select for highest growth rate, and show how such a cellular site of 'growth control' was identified. By applying pH-auxostat cultivation to the already fast-growing yeast Kluyveromyces marxianus for a sufficiently long time, we selected a strain with a 30% increased growth rate; its cell-cycle time decreased to 52 min, much below that reported to date for any eukaryote. The increase in growth rate was accompanied by a 40% increase in cell surface at a fairly constant cell volume. We show how the increase in growth rate can be explained by a dominant (80%) limitation of growth by the group of membrane processes (a 0.7% increase of specific growth rate to a 1% increase in membrane surface area). Simultaneous activation of membrane processes may be what is required to accelerate growth of the fastest-growing form of eukaryotic life to growth rates that are even faster, and may be of potential interest for single-cell protein production in industrial 'White' biotechnology processes.