Nature of the electrode (metal)
The nature of the electrode refers to the type of metal used. Different metals have different tendencies to lose or gain electrons, which affects their electrode potential. For example, metals with a higher tendency to lose electrons, such as zinc, will have a more negative electrode potential compared to metals with a lower tendency to lose electrons, such as copper. Therefore, the nature of the electrode does affect the electrode potential.

Temperature of the solution
The temperature of the solution can affect the electrode potential. An increase in temperature generally leads to an increase in the electrode potential. This is because higher temperatures provide more energy for the redox reactions to occur, resulting in a higher potential difference. Therefore, the temperature of the solution does affect the electrode potential.

Molarity of the solution
The molarity of the solution refers to the concentration of ions in the solution. The electrode potential is directly proportional to the concentration of ions. As the concentration of ions increases, the electrode potential also increases. This is because a higher concentration of ions provides more opportunities for redox reactions to occur, resulting in a higher potential difference. Therefore, the molarity of the solution does affect the electrode potential.

Size of the electrode
The size of the electrode does not affect the electrode potential. The electrode potential is determined by the nature of the electrode and the conditions of the solution, but not by the size of the electrode. Whether the electrode is large or small, the electrode potential remains the same as long as the other factors are constant. Therefore, the size of the electrode does not affect the electrode potential.

In conclusion, among the given options, the size of the electrode does not affect the electrode potential. The nature of the electrode, temperature of the solution, and molarity of the solution all have an impact on the electrode potential.