I have never grown them from seed, but I did gather some seed from my Arum italicum this summer the same way you described. You may want to use rubber gloves while doing this because the berries contain something that can irritate the skin. I learned the hard way. When I got through my hands felt like they had a million needles in them. They are a beautiful plant. I have had mine in the same place for about 5 years now and they have formed a clump 2 feet in diameter. I would not try to move them to a new location because they multiply and form so many babies that you would never get all of them. I was going to relocate mine this summer and gave up after finding about 20 nice size bulbs and about 200 babies. I ended up throwing everything back in the hole and covering it up.

I've had mine for 8 or 9 years now, and while they have spread, I'd hardly call them invasive. I've never divided them either. I recall something about once harvesting the seeds/berries that they need to be planted very quickly, but don't quote me on that. I haven't investigated that any further, since I'm really not impressed with the berry display, but more interested in the winter foliage interest.

Just a note about my experience with Arum italicum seeds. I received some in early April after I begged for them in the Aroid Forum (Shame-on-me). They were from fall '05 harvest and were the dried, whole berries. I removed the hulls by rubbing them and winnowing, and planted in a flat of ordinary 'Miracle Gro' potting soil about 1/4" deep( about 500 seeds, a generous gift). Kept moist and in a shady spot under a shrub, they began to sprout in mid May, about 5-6 weeks after planting. Currently have about 25% germination, but more are still breaking through.

George

After you take the seeds out, before you sow them, wash the seeds repeatedly with running (or at least moving) water, because the berries contain germination inhibitors you need to remove from the seeds before sowing. They seem to need a warmth period first, as mine didn't germinate when I sowed them cold, but did the next year, once the temperature dropped. By the way, I also have read that the seeds are short-lived, but I have serious doubts about that, since my two-year-old seeds (when sown, not while germinating) germinated with a 100% germination rate, which was more than the fresh ones.

A neighbor gave me some garden debris for compost and it had all these little white bulbs in it. They sprouted arum italicum all over my vegetable beds! So maybe don't even both with the seeds... dig up and divide the little bulbs. They're definitely invasive here.