In a MOSFET if VGS is kept constant then VDS is increased till entering a saturation mode, a pinch-off accrue near the drain. This indicates that the E field between the gate and the bulk is not evenly distributed due the increasing positive potential at and near the drain region. This phenomena will also affect the resistivity of the channel. Does this means that the resistivity near the drain have the highest value? If so the dissipated power is mostly generated near the drain?
I simulated for a year electronic semiconductor devices.
Channel resistivity is a 2D function: ρ(x,y).
ρ(x,y) changes as VDS change.
To answer your question:
Does this mean that the resistivity near the drain have the highest value?
Yes, it does.
Is the dissipated power mostly generated near the drain?
Yes, it is.
The external circuit will see the overall channel resistance R which is the 2D integral of ρ(x,y).
You increase the channel width W, you reduce R.
The electric field vector E(x,y) and the current density J(x,y) are 2D functions as well.