They are very sensitive to growing conditions. If I fertilize and water heavily, my white Japanese anemones will reach 6 feet and more, even in full sun. This is a stunning sight, by the way. If they are starved and infrequently watered, they will be 1-2 ft. tall. If they don't get some sun, they will die out after a couple of years. But they don't need full sun.

I don't know if the pink ones behave the same as the white.

Mine are 3-5 ft depending on location. They may self-seed. They seem to come back well every year so far, and bloom from about now until frost.

More than one kind is grown as Japanese anemone. Most spread rapidly by creeping rootstocks, possibly that is the "self-seeding" although you may be saying you think you have seedlings as well. Anyway, not a good plant where you have smaller things nearby that you don't want invaded.

East Asian in origin so extra summer moisture would be expected to improve results here in Mediterranean climate of Pacific Slope.

Thank you all who responded to the question about the pink anemone. I think the location here is definitely a factor, sun vs. partial shade.

Some of my Anemones popped up in places a long way from other Anemones, so that's why I think they self-seeded. Maybe I actually brought a piece with me when transplanting something else. They are bad about over-running other plants.