Remove them once finished if it looks untidy. If left on, the small white berries that stud the stems look attractive though. They are not poisonous so don't worry if kids about. The black seeds inside germinate easily too.

The top of your plant will be terminated now but two or three new shoots will emerge near the base of the flower stalk and produce a couple of branches. Over time after this has happened many times, they can develop a domed branched crown.