They don't fight. They each monitor the battery and supply power if the battery is low.
You can hook up any number of various and assorted charging systems to one battery or bank and they won't butt heads. It's like having a bunch of different air compressors hooked up to one tank. Each compressor will shut down when the pressure in the tank is high enough.
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Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker