The breaker has nothing at all to do with protecting anything other than the wire itself, so to answer your question, need to know the wire size  Normally like 40 or 50 amps......tops.....

The wire should then be sized for the loads it will be required to run, so sort of a chicken before the egg thing

GT

#10 wire (stranded) is good for about 30 amps, 35 if you feel lucky 

If you were to up the wire to #8, you could pull 40 amps without issue.

Be careful if you have an ammeter (hope you don't), the charging wire would go from the alternator all the way to the gauge and back to the battery, this is where most catasrophic failures occur. Especially when the alternator is upgraded....

Voltmeters do not have this problem, but the wiring should be rerouted to the battery....

GT

I was gonna say, 40amps?, I have 2 breakers and they're both 30 amp.

Ray

Ray, I don't make the rules, I share them   

  GT 

Well
I installed another breaker for the stereo system (100amp) with its own lead from the battery, So the only other thing thats left are my gauges,Alt.....e.t.c.. how about isolating the alternator on it own breaker, maybe two 30's or one 30 for the alt and one 15 for the console.