Think i have a short???
Any suggestions where i should look remember your talking to an amateur.
1977 f-250 4X4
as i live and breathe they've always gotten me home!!!
Secondly the battery is necessary to "supplement" the alternator output when the truck is at idle and a large load, like headlights, is applied. No battery and the engine will most likely die

Now for your problem
when you say it dies I assume you mean the battery is going dead. If so disconnect the negative battery wire and connect a 12 volt light between the battery neagtive wire and the battery negative post. If the light glows you have a "parasitic draw" on the battery. Or as many people like to say a "short" 
So with the light still connected, disconnect the plug on the voltage regulator. If the light goes out get a new regulator, if not. Disconnect the alternator, if light goes out it is the alternator if not. Start pulling fuses one by one til the light goes out. When the light goes out that is the circuit that is killing your battery.
Oh yeah you do not need the truck running to do this check. Also make sure the interior light is off and the under hood light also, as these can lead you on the proverbial wild goose chase.
Sparky
First, I agree with Sparky. Running your vehicle off the alternator is a bad idea. The battery is not only a storage device, it also acts like a big capacitor. That means it works as a filter for the alternator. The alternator is an AC generator with a bridged diode rectifier usually built in to it. It's output is not DC until it is filtered to remove ripple. Remember, the alternator's primary purpose is to charge the battery. On an older vehicle such as yours you can probably run the engine off the alternator without doing any damage to the electrical system (not too good for the alternator though). However, if you do this on a newer vehicle you might cause some problems. Modern electronics do not like unfiltered current and may stage a revolt.
Now for your problem. When you changed the alternator did you change the voltage regulator? If not, you should. They should always be changed together. If that doesn't fix it, check the wire from the primary side of your coil. If there's any doubt, replace it. For any more advice I would need more info such as what kind of ignition you have. Points or solid-state? Engine size? Good luck and keep us informed - BUBBA
You can test your alternator output by using a DVOM(mutlimeter). Set it to dc volts put black lead to ground and red to power wire at back of alternator. If the system is working you should get 13-14volts there. And you can check it at your battery. Battery voltage should be around 12.5volts or so depending on battery charge.And when running it should go up with all you lights,radio and heater fan on. Basically putting a load on the system. This would tell you if your voltage regulator is picking up the system load to keep the battery charged. But like Sparky and Bubba said it's not a good idea to run your truck with the battery disconnected. Hope this helps.




