10K generator starts off the engine batteries. I have 170 amps of charging from a 100 amp separate charger that's part of the four battery/1000W PSW inverter for the refer and a sat receiver/dvr 24/7 plus a led TV maybe four hours/day.
The six house batteries are on my 2000W MSW inverter/100 amp charger that only put out 70 amps max on generator power. They power all 12V items like lights, 2 Fantastic fans, AquaHot, and the inverter for a 40" led TV and sat receiver maybe 4 hours/day. Will often heat lunch with the micro using the inverter. With everything possible turned off (including the inverter) there is still 2.5 amps parasitic draw on the system, most of which is from the BigBoy relay. On a sunny day this system will get 10-12 amps of solar charging. I can tie both battery banks together which when boondocking I usually connect together. The BigBoy ties the engine batteries into the system mainly when the solar gets the voltage above 14V.
Before getting on the road after boondocking for several days I'll run the generator for at least an hour to decrease how long the alternator will have to put out 100+ amps.