Please help identidy

[Francois]

I have these growing from my live rock. At first I thought it's mermaids cup now I'm unsure.
By the look of things it grows a long branch which then roots itself.
The ends were flat but now I see it balloons. Any help please?

 

[Mike&Terry]

Looks like Grape Caulerpa.

 

[Penny]

How do you get rid of grape caulerpa? Is there anything that eats it??