This is related to this question
It is the case of a simple cantilever beam having a uniform rectangular cross-section.
cantilever beam composed of separate planks - taken from 
The question in the original post was What happens if we split it along its longitudinal axis? @sudhir asked What would happen if the beam was loaded uniformly
In the original post the deflection of the coupled beam with the decoupled beam was
$$ \delta_{decoupled, concentrated} = 9 \delta_{coupled,concentrated}$$
If you change to a uniform load then with respect to the relative deflection of the coupled/decoupled would remain the same. i.e. $\delta_{decoupled, uniform} = 9 \delta_{coupled, uniform}$
Of course, the total deflection would be less because the formula for $\delta$ will change(see link ).
Assuming that the distributed load is $w=\frac{P}{l}$ (so that the total load is the same for comparison purposes:
$$\delta_{coupled, uniform} = \frac{w\cdot l^4}{4\cdot I_{coupled}}=\frac{P\cdot l^3}{4\cdot I_{coupled}} = \frac{3}{4} \delta_{coupled, concentrated} $$