The molecule that serves as the common branch point for both anaerobic and aerobic pathways is pyruvate.

Here's why:

* Glycolysis, the first stage of both aerobic and anaerobic respiration, breaks down glucose into two molecules of pyruvate.

* Anaerobic respiration occurs when oxygen is not present. Pyruvate is then converted to lactate (in animals) or ethanol (in yeast) through fermentation.

* Aerobic respiration occurs when oxygen is present. Pyruvate enters the mitochondria and is further broken down through the Krebs cycle and the electron transport chain, yielding ATP (energy) and water.

Therefore, pyruvate acts as a crucial junction point, determining which metabolic pathway the cell will follow depending on the availability of oxygen.