I'm still kind of knicked about these "instant battery chargers" for your car. I'm not talking about the ones that essentially have a car battery inside or hook up to your house power that actually work, I'm talking about the ones that essentially have the battery from your cordless drill in them and decidedly do not.
If your battery is ever so slightly low it *might* work but they market them like you can start a car with a dead battery with them. I can't even start a car with my giant craftsman instant start if the battery is dead.
This is a lot more feasible than it seems. You would be astounded how much power you can pull off a power tool type battery (cell Li-Ion optimized for power, not energy, density). Something like 6-7 years ago the battery shop I worked with was pulling 75A at 19V off a pack for a cordless drill. That's 1.4kW (comparable, btw, to what you can pull off a 15A wall socket). They were willing to warranty it for 2-3 years under essentially continual charge/discharge usage (professional craftsman setting).
I'm sure battery tech has improved at least some since then, and you can go quite a bit higher without compromising the electrical/personal safety of the system. You'll just wreck the battery after only a few dozen cycles. That's OK for this application. Figure you can get a few hundred amps at a nominal ~19V off a high-quality Li-Ion pack sized for a typical cordless drill with no problems. With a reasonably efficient switch-mode converter, you can hit 12-13V at currents comparable to the CCA rating of a typical car battery and with less effect from lower temperature to boot.
Now, you're not going to charge your car battery this way since there's not enough energy in the tiny portable jump-box, but hooking up a little box the size of 6 decks of cards stacked on each other and weighing less than 10 pounds to your car to "jump-start" it (and allow the alternator to charge the battery in the car normally) is amazingly feasible.
Obviously this won't work if your car battery damaged or so discharged as to be essentially shorted. In that case, all the juice from the jump-box goes into the battery and not the starter motor. Some of the portable jump-boxes that I've seen recommend disconnecting the car battery if you have trouble starting for this reason.
Some of them also work by re-charging the (presumably) dead-but-not-damaged (just left your headlights on or similar) car battery through the cigarette lighter port. They usually recommend you leave it plugged in for several minutes for that to take place. These are usually touted as allowing you to jump-start your car without opening the hood. The problem with this trick is that it only works on a mildly dead battery. There's not enough energy in such a small Li-ion pack to charge the humongous lead acid in your car up enough to run the starter motor. The reason the direct connection method works is that, while the tiny little portable jump-box has comparatively little stored energy, it can dump it all rather quickly.