Electronic switches rated for 300A @ 12VDC
About big transistors

Well... big transistors are still transistors and act like transistors.

There are dedicated ICs with logic input to drive high power transistors. These drivers are designed to charge (turn on) and discharge (turn off) transistor gate very fast. Transistor gate can be considered as capacitor. In big transistors gate has higher capacity, there are higher charge and discharge currents, but... idea is the same. 

When gate is charged - transistor is turned on. When gate is empty - transistor is turned off. If gate is partially charged - it is partially turned on and it has some resistance which causes power loss which is very undesireable when switching high currents.

High power transistor drivers are usually more complicated because they have some additional protection to prevent fire or other damage in not normal conditions (like power brown-out) etc.

Big transistor drivers

If you are looking for big transistor driver - you can google for "IGBT driver ic" I found:


ISO5500 from Texas 
MC33154 from Motorola
AUIR08152S from IR


First one is not suitable for you (datasheet says "transistors up to 150A", but maybe someone else will be interested.

Last one is for automotive, maybe it will be suitable for you, but everything depends on transistors you use.

Most of ICs like these can drive very big MOSFET and IGBT transistors. They usually need positive and negative supply, because negative voltage applied to transistor gate can discharge gate faster (gate can be considered as capacitor), and transistor can be turned off faster to reduce switching power loss ("transistor partially opened" time is shorter).

Power supply for big transistor driver and driver itself should be very reliable, because if it fails during transition (turning on or off) - your precious expensive transistor will blow up.

Safety!

Few important things when you are playing with 3kW circuit:


make sure you have fire extinguisher :)
never(!) allow your transistor to be partially open at high current (like 300A) because it will explode
use some protection glasses, some shield/casing for circuit and/or keep safe distance
use some kind of "kill switch" that turns off everything in case of fire or other problems


Keep in mind that alternator is huge inductance in circuit

You may have problems with alternator and voltage regulator in it if you switch very big load very fast. You may have to modify alternator voltage regulator to reduce excitation current when you are switching load. Alternator has huge inductance and there will be huge back-EMF when you suddenly connect or disconnect 250A load. So... maybe your circuit is 12V, but back-EMF can be much higher.

Troubleshooting big transistor driver

Using oscilloscope to see what is going on between drain and source while switching is highly recommended.