prasansurana said:
Will the alternator supply half of the current it is producing to each battery?
No. Is the isolator just a switch or is it a smarter device? Often dual battery isolators restrict charging current to the aux until the primary is full. If yours is one of those, then there's your answer.
If the isolator is just a switch, and it is closed, then the answer is that the batteries will share the current depending on their state of charge. And given that no two batteries are the same (certainly not a 80Ah and a 180Ah), their state of charge will not rise in unison.
The usual way to figure it out is a bit simplistic but pretty useful for a first approximation: the batteries are modelled as a voltage source whose voltage rises somewhat linearly with state of charge, in series with a resistance that is fairly small (say a tenth of an ohm) and reasonably constant (actually varies with temperature and other things). As the batteries absorb charge their internal voltage will rise at different rates. Because the voltage across the batteries has to stay the same (since they're wired in parallel), they will draw dissimilar currents.
In practice, the larger capacity battery will likely have a lower internal resistance so will draw more current to begin with. As its internal voltage rises, it will start to draw less. As both batteries approach 100% state of charge, they will continue to draw current according to their respective internal voltages. If the 100% charged voltage of one battery is lower than the 90% charged voltage of the other battery, the charged battery will continue to draw current, wasting it as heat. That's why dual battery systems with dissimilar batteries should have a smart isolator that only charges one battery at a time.