Pink Japanese anemones spread freely, but they’re so lovely for so long that it’s hard to be strict with them.
Recently I read a popular local garden column, urging removal of self-seeders to protect the purity of the garden’s design. To each his own. Personally, I enjoy mother nature’s whimisical plantings and actually encourage them. If I’m unhappy with where a foxglove or malva sprout I can always remove them. But, my garden would be much duller without the summer ruffle of wild daisies or the graceful waves of anemones softening the evergreen shrubs.