There are two distinct limitations to a pot still; the relative lack of reflux and the fact they run in a time-consuming batch process. In trying to overcome these two challenges, Aeneas Coffey patented the first column still design in 1830 and ushered in a new era of continuous spirit distillation aimed at efficiency and rectification (the cumulative effect of reflux).
The variety in design of column stills is great, but in principle, they work in the same way. For the sake of brevity, we will imagine a single column that is already up and running.
Preheated alcoholic mash is fed into the base of the still. The heat source is most commonly a steam heat exchanger, although many Rhum Agricole stills are direct heated and some multi-column installations use steam injection.
There is a constant flow of vapor rising up through the rectifying plates, and a flow of liquid down the plates. Distillation happens on every plate and the fractions are separated across the height of the still. The most volatile fractions rise to the top of the still and pass out as heads. The less volatile fractions are continuously drained at one of the bottom plates as tails. Your hearts cut is tapped somewhere in between; closer to the top if you want a more rectified spirit (lighter marks, around 90-95% abv) & closer to the bottom if you want to retain more congeners (heavier marks, around 65-85% abv). When we speak of weight in rum, we are talking about the amount of liquid that is neither ethanol nor water.
As long as the total volume of liquid entering the still is equal to the fractions leaving the still, you have achieved dynamic equilibrium. Continuous distillation is a bit of a misnomer though since stills periodically have to shut down for cleaning and repairs.
By far, the biggest variable in this process is the height of the still, and at which plate you choose to take your hearts cut.