There are many examples of MOSFETs that, if cooled properly, can handle sustained currents upwards of 200A. Many of there come in surface mount packages.
How is it possible to design a PCB that is capable of handling the 200A drain current?
It seems like you would need to solder theses directly to a copper plate.
Example datasheet: IRLB3813PBF
Best Answer
The maximum drain current is more theoretical than practical. Let us delve deeper.
The datasheet says 260 amps with the case temperature of 25°C, and RDS(on) of 2 mΩ.
So the transistor must dissipate 260 * 260 * 0.002 = 135 watts while maintaining a case temperature of 25°C. That may not be physically impossible, but it would require a totally unreasonable thermal solution (heat pipe or liquid cooling or something outrageous). So, actually, it is not a realistic continuous current purely for thermal reasons.
Even at the lower rating of 190 amps at Tc = 100°C, the dissipation will be 72 watts. It will be extremely challenging to maintain a case temperature of only 100°C while dissipating 72 watts.
In addition, if you read the fine print, the datasheet actually has a note that says the package maximum drain current is 120 amps, and that the 260 amp figure is just based on a simplistic thermal calculation using RΘjc (thermal resistance from junction to case).
So in the end, the so-called continuous current rating is not even intended to be realistic. It may be useful for comparison with other transistors using the same rating scheme. But other than that you will most likely need to do thermal calculations based on your actual operating conditions. So you should be looking at the maximum junction temperatures and the various thermal resistances and RDS(on) rather than Id continuous. Don't neglect the importance of the PCB footprint area in thermal design of SMT devices. Often they are intended to transfer heat through a large SMT pad on the PCB.
Some MOSFET datasheets now provide current limits based on thermal resistance from junction to ambient, which are more directly realistic/useful.