Common liverwort

Jopy, I added photos with "umbrellas"! :))

Thank you, bg11a1! :)

Congratulations

yes! :)
I'm looking forward to it, too! :))
I also have found one liverwort in the forest (different species) and I'm waiting for its umbrellas, too :))

That's what I thought! In umbrella like structure will develop sporas... Looking forward to see it :)

They are called gemma cups, and, yes, they are for asexual reproduction :)
"...detaches from the parent and develops into a new individual" http://en.wikipedia.org/wiki/Gemma_%28bo...
later this liverwort will produce umbrella like structure for sexual reproduction, I will try not to miss that :)

I'm not very familiar with mosses, are these plate shaped structure reproductive organs?

Yes, thank you! :)
And it is growing in my backyard :D (on the border, to be more precise) :))

Pretty!