You mix AgNO₃ and KI in the following molar ratio

	AgNO3	KI
I.	1	1
II.	1	2
III.	2	1

Fixed layer of the electrical double layer migrates to cathode in

I. $\underset{1}{{\mathrm{AgNO}}_3}+\underset{1}{\mathrm{K}}\mathrm{I}⟶\mathrm{AgI}\downarrow +{\mathrm{KNO}}_3$

Being in equal stoichiometric ratio, Agl is precipitated. It carries no charge and, hence no migration

II. $\underset{1}{{\mathrm{AgNO}}_3}+\underset{2}{\mathrm{KI}}⟶\mathrm{AgI}+{\mathrm{KNO}}_3$

KI is in excess hence Agl adsorbs common ion of KI (ie. I^-) 

$\mathrm{AgI}+\mathrm{KI}⟶\left[\mathrm{AgI}\right]{\mathrm{I}}^{-}⋮{\mathrm{K}}^{+}$

             Fixed layer Mobile layer

Fixed layer carries negative charge and moves to anode plate.

III. ${\underset{2}{\mathrm{AgNO}}}_{ }+\underset{1}{\mathrm{KI}}⟶\mathrm{AgI}+{\mathrm{KNO}}_3$

Agl is precipitated and AgNO₃ being in excess, Ag⁺ is adsorbed on AgI.

$$\begin{gathered} \mathrm{AgI}+{\mathrm{AgNO}}_3⟶\left[\mathrm{AgI}\right]{\mathrm{Ag}}^{+} : {\mathrm{NO}}_3^{-} \\ \mathrm{Fixed} \mathrm{layer} \mathrm{Mobile} \mathrm{layer} \end{gathered}$$

Fixed layer carries positive charge and migrates to cathode (-ve) plate.