It's been a very interesting (and lengthy!) discussion and a fun subject. Battery power for car amps in a home theater seems most likely way to get the best sonic performance out of car amps, but the cost of the batteries and a battery charger will negate any savings in buying car amps over home theater amps and you'll have to deal with the hassle of shutting the system down and recharging the batteries (with the duration between charges dependent on the number of amps and number of batteries). You would need at least three or possibly four of the batteries that painttoad suggested (at close to $150 a pop) plus charger(s) to yield enough power for a few hours of intense home theater use. That's a lot of cost and a lot of hassle - a Model 7100 would be cheaper than batteries, charger(s), and amps to provide comparable power.

A power converter of some sort is a much more user-oriented solution to operating a car amp on 120VAC power, but again you are looking at incurring a healthy cost. I stumbled across tekdredger's very nice tutorial link earlier today while looking for information on amp power supplies, and it does seem to be a very good insight into the power side of amp design. It also looks like a great deal of work and cost when home theater amp makers have already done the work and tucked it into a metal box.

As far as car amps versus home theater amps in general, I've noted at least a few clear differences. Car amps are routinely rated at 4 ohms, whereas home theater amps are usually rated at 8 ohms (sometimes 6) - this makes the car amps seem a good bit more powerful dollar-for-dollar, but in a home theater system that routinely has 6 ohm and 8 ohm speakers you'll have to adjust car amp power ratings downward accordingly. Also, there should be a cost difference watt-for-watt between the two: home theater amps are saddled with a large transformer (crammed full of expensive copper wire) and rectifier required to produce DC power. Taking into account the cost of such a power supply and the differences in power rating, you can get a good home theater amp from several respectable manufacturers (including Outlaw) for comparable or less money than required to buy car amps and arrange for power supplies or batteries.

I would not want to pursue the project and I don't know that it can be done for less money than a home theater amp, but it would be a very interesting sight to see if somebody went through with it.