These white stones seemed to be all around randomly - so I thought I'd better look them up once I got home. They are the Stone Pigeons made originally by Simson von Seakyll for a group exhibition called "Minu kallis paranoia" (My dear paranoia). I think we are supposed to come across them and think of them as secretly talking to each other. I didn't really see them that way - or I guess if they were talking to one another they were saying nice things.
There were 97 of them made initially. Pigeons like these are indeed scattered all over the city, but they aren't random - they serve as barriers (ie: places one shouldn't drive). I read that lately many of them are being removed because people are either moving them, stealing them, tripping over them or driving into them. I think they are pretty cute.
Here's another cute guy that lives in Tallinn. His name is Black Angus.
Here's a better photo of him - from the internet...