The maximum current can be drawn from a cell if the external resistance R = 0.
Current flowing through a circuit
The current flowing through the circuit is given by the formula
r : the internal resistance of the cell
R: the external resistance.
The maximum current can be drawn only when external resistance is zero.
When current is to be drawn at max then the conducting wire rating comes high such that resistance is less.
Resistance and Area
Resistance R=ρ x l/a
ρ = resistivity constant
a=area of cross-section
Hence, if the area of cross-section increases resistance decreases by increasing the rate of current to flow.