Car stereo system into home stereo system?

You would need a 12v to 110 voltage converter box similar to the ones linked below...the size of the unit you need is determined by how many amp your trying to push the more amps the more robust the converter box needs to be.

It's possible to do this....that being said,rather than using a car battery you need to use one of two options,

1,use a high amperage 12 volt power supply,,,10 amps would be more than adequate in most cases. A lot depends on how much equipment you are driving. Remember that most car speakers are 4 ohm vs home speakers that are normally 6-8 ohm. 4 ohm loads are going to be a bit harder to drive. The power Supply you need will probably be found at an electronics surplus store or salvage store. A new one would be very expensive....3-500 dollars. 2. You could buy an ac to dc power converter. (110 ac-12v dc) these aren't cheap either...at least in the power range you would need. Also,since these inverters are normally used for applications other than audio,they can potentially create some serious noise problems....they are not shielded and typically use cheaper components than a home audio amplifier, I have done exactly what you are considering and I was less than thrilled with the sonic attributes and the cosmetics of the final product.

It's a lot of trouble for the work,,,,,,oh,I almost forgot.....don't forget that your car speakers use the door panels or dash as an enclosure. You will have to design an external box for your car speakers......that in itself is a lot of work. Don't mean to discourage ......when it comes to audio almost anything can be done,,,,you just need to decide if it is really worth the time and money to do it based on the results you will obtain,

i would suggest looking into home theater amps like this one

http://www.sonicelectronix.com/cat_i832_home-ampli...