the lead acid battery in a car provides power to operate starter motor, lights, radio, etc when engine is off
when engine is on, said battery is charged to the level determined by the voltage regulator
when fully charged, the alternator provides less power
so it provides power (discharge) and absorbs power (charging)
other than homework problems to enforce understanding of Kirchoff's Laws,
i have never heard of anyone putting power supplies in anti-parallel, as noted by FvM
what is behind your question?