Do really alternator power all the electric components in car?

The battery powers the alternator which then sends that power back to the battery and the rest of the vehicle, but the alternator is only as good as the battery is: so it is a joint effort!

The batteries only purpose is to start the car. It also does and do help maintain an even voltage. But the alternator provides power for absolutely everything else in the car and part of the power from the alternator goes to recharge the battery and to maintain the batteries charge while you're driving so all your lights heaters everything else is controlled from the alternator.. the more electronics added to the car the bigger the alternator you need the days of having a 35 amp alternator to power your car is over many cars are now using alternators up to 200 amps to power the electronics in the car. If your alternator on your car dies depending on the car and what electronics you are using you can only drive your car from between 15 minutes to just over an hour never mind before your car shuts off. Alternators produce ac current and uses a set of diodes in the alternator to convert it to DC.. an unregulated alternator can produce a lot more voltage than your car can handle and it will blow out all your lights but you have a regulator that limits the electrical field in the alternator so that it produces the proper voltage somewhere between 13 and a half to 14 and 1/2 volts on average

while the car is running the alternator charges the battery and also feeds the proper voltage to the engine management components

Why don't you disconnect the alternator and see which accessories don't work. Hint; what doesn't work when the engine isn't running?

The SOLE purpose of the battery is to power the starter. Once the engine is running, the alternator should power all electronics AND recharge the battery.

no the alternator recharges the battery , the battery helps powers everything .

The battery not only starts the motor...it also acts as a ballast to stabilize the 12 volts all electrical components need. An alternator without a battery in the system will go into maximum output which can be as much as 18 volts. That would fry all the modules and the PCM. That's why you should never remove a battery cable with the motor running on cars with computers in them.

A battery is needed to start the car. Even hybrids rely on the 12v battery to run the systems ( not strictly starting the engine).

Before F1 cars became hybrids, you would see them wheel a battery onto the grid to start the cars. They had no need for them once the race started .

The battery acts as a buffer and store for the electricity the alternator provides, and everything is actually powered by it.  The alternator keeps the battery charged.  They work together.  Do NOT try to run the engine without a battery in circuit, you risk wrecking the electrics and electronics. 

You 'learned' incorrectly, all the alternator does is keep the battery charged.