Well I can't say for sure how to grow 'em big in California. I would start out by checking the Sun Tolerant hosta list on this page. Hostas are really more heat intolerant than sun intolerant, but heat and sun usually go hand and hand. The hostas on this list will be more apt to survive in higher temperatures. Hostas are happiest in cool, moist areas.
I can tell you what I do in my own hosta garden to get hosta leaves bigger than my head. Here are my ten steps:
4. I usually do not fertilize my hostas, if I do I use a worm poop fertilizer, such as Terracycle (can be found in stores), once a year in spring.
5. Get rid of the slugs and other pests. I use sluggo, but there are organic ways to get rid of them (one involving going out at night, picking them off hosta, and putting them in ammonia ). For deer and rabbits, I use Liquid Fence. We don't have a huge deer problem, they usually just get into the garden in winter and early spring.
6. Water some more
7. If they are not happy where they are (give them at least a year somewhere) don't be afraid to dig them up and move them to a spot where they will be happy.
8. Water some more
9. I don't divide unless they have grown too big for the spot I have them in. Despite the myth, hostas do not require dividing.
10. Buy hosta from reputable people or nurseries. There is a hosta virus out there, and I have seen it at many nurseries (especially the big box stores). Be aware of the hosta virus (HVX), the symptoms and signs, and avoid nurseries where you see it. Another threat to hostas are nematodes, which usually will not show until mid-summer to fall (depending on where you live, the warmer the earlier signs will show). Maybe tomorrow I will list mail order/internet sources for hostas which I know to be safe.
Hope this helps, as I love to spread the hosta love!