current, voltage, ampers issue

Do the big three to get the most power available from the stock alternator.  If you can't get satisfactory results after that, look into obtaining a high output alt.  Read the sticky posted above for more info.  Also read the What is a Proper Ground sticky.  Fuse the power wire to the capacity of the wire; don't fuse it with an expectation of blowing the fuse so you can be satisfied that the system pulled more than 80 amperes to do so.

Put this website in your favorites folder:  www.bcae1.com  There is a tutorial on measuring amplifier output there, among other things you'll want to learn about.  Send for the CD for more detailed explanations than what shows on the site.

You have to realize that most of what you hear from other people, as well as most of the specs that you read, are simply gross exaggerations.  When one has an amplifier that is "rated" at XX watts, that doesn't mean that it puts out that many watts.  Numbers like that are truly meaningless in today's car audio market.  The reality is that in your daily listening you are likely using one to ten watts from the amplifier.  Once you're at ten watts, you can quickly increase the power demand (and likely the subsequent power output) with just the slightest touch of the volume knob.  And the levels of power at a certain point may just make the sound unlistenable, well below the 1000 watt "rating".

Look at it like this:  the speakers you listen to are designed to deliver a certain decibel level with only 1 watt of power applied when listened to at a distance of one meter.  To achieve a noticeable increase in loudness, you have to apply double the power (that's +3 db).  So say you are listening to a speaker whose output is 87 decibels at 1 watt;  at 2 watts the output is 90 db, at 4 watts it's 93 db, 8 watts goes to 96 db, etc.  And there is likely an additional increase in sound level due to the car environment you are listening in ("cabin gain").  So with this you can see that only 8 watts provides a sound level that when listened to for a prolonged period of time would contribute to eardrum damage.  Another good sticky subject.

As you continue the math that I started, you see how quickly power jumps at those highest levels of output;  e.g. 64 watts to 128 to 256 to 512.  And keep in mind there is still just a +3db sound level increase at each of those incremental changes.  The difference between the 500 watts and the next jump to 1000 watts is not worth consideration.  It is just a rating, whether fairly measured or not, that serves to place the amplifier in competition with a field of other amplifiers who are similarly rated.  A much more valuable datum would be manufacturer quality...not power rating.  A clean 50 watts is more valuable than you might think, because a well designed and built amplifier will have the reserve capacity to provide power for the peaks as well.

With all that, it should be a rarity that you could melt an 80 amp fuse while listening to your system.  The fuse is there to provide the necessary safety factor should an accident occur;  it will keep the wire from being used as a conduit for the battery's reserve amperage to be unleashed into the chassis of the vehicle or through whatever other conduits it can find.  The result of this is usually catastrophic.  But the value of the fuse should be whatever the wire is rated for, as a rule. 

When "People claim they are running >1k watts off a stock alternator"  you should realize that they are merely using some gear that has a 1k watt rating, not that the gear is actually providing that power level.

The Knukonceptz 4 ga. wire is sufficient for that amplifier.  Use a beefier wire if it will make you happy.   And I have seen wire ga converters like you asked about;  look through some of the supply houses or ask at your local car audio installation shop.  Or simply use a distro block  which will provide outputs for future additions to the system.

Did I miss something here?

If you arn't blowing an 80A fuse why would you "get a proper fuse for the 0 gauge".  By the recomendations in this thread that would be a 350A fuse.  Fuses are meant for protection and if you arn't pulling over 80A fusing your power wire at value 4x more then that would be a terrible idea.

"Fusing the wire" is a bad idea for 10ga - 4ga but once you get passed that it is a much better idea to fuse for your expected load.  The idea of a fuse is for it to open as quickly as possible in the case of a catostrophic disaster (ie short to ground).  The larger the fuse value the longer it is going to take for the fuse to open. 

Take a look at this 32vdc ANL fuse data sheet:  http://www.cooperbussmann.com/library/bifs/2024.PDF

One thing the datasheet won't tell you is that his is a $68 fast acting fuse.  This isn't a $10 cheapy that you will most likely put in your car.  This fuse will naturally react faster and in a more predictable manner then a "cheap" fuse.

Let's assume:

1. Battery

For a 350A fuse to blow in less then 1/2 second (which is still too long in my oppinion) you will need to be able to supply close to 2,000A of current to it!

For a 350A fuse to blow in 0.1 seconds which is where I would be comfortable you will need 3,500A of power!!!!

Again, to summarize - fuses are protective devices to not only protect the wire, but the battery as well.

The longer your battery is "crowbarred" the higher the chance electronic parts will be fried

Using a large fuse, IF you need a large fuse, is a nessessity.  But, using a large fuse just for the sake of not spending a few mintues calculating your expected load is sloppy and very risky.

Correct me if I missed something here, but if you have an 0 gauge power wire with a 350 amp fuse, then if it shorts to ground, the current flows through the 0 gauge until the fuse blows.  Why would the current surge through the entire system?  Your load from the power source would be the 0 gauge.  Yes, I can see that all the electrical systems share the same ground, but with your reasoning, it would happen in all occurances with over current conditions.  If your 20 amp cigarette lighter shorts out, then why doesn't the 5, 7.5, and 10amp circuits blow in the vehicle as well?  If, for some strange reason, the high current demand pulled from every circuit, then the individual fuses would blow to protect the electrical equipment in the vehicle.  It's the same scenario why one shorted circuit doesn't effect other circuits in the system, but just on a grander, more, extreme scale.

You are correct the full current would only flow through the fuse, you wouldn't pull that amount of current through every circuit in the car.  But, every device connected to the battery would be effected by the drop in battery voltage and the immediate loss of current to the device.  Every cap in every power supply of every electronic device in the car would backfeed voltage back to the battery, as the battery tries to provide the absolute most amount of current as possible.  This is very hard on car power supplies and the likely hood of them failing would be great, especially if it is an intermittent short to ground - something a 350A fuse would never protect against.

You can't compare a short to ground through a 15A cigarette lighter jack to a 350A short to ground through a 0awg cable.  If you think you can, you missed the entire point of the 10+ second delay for a 350A fuse to blow vs. the 0.001 second (estimate) of a 15A fuse to blow when shorted to ground.

When dealing with any electronic device with a power supply (ie car battery) about the worst thing you can do is short out the power supply (ie car battery).