What happens to my processes?

I was logged in a computer of mine in my network. I got a process in background, when by mistake I closed konsole and logged out. When I logged in again, my background processes were still running, but when I tried to kill them it said I was not their owner. I was logged in with the same username though. So I have to ask, what happened to my process? Were they really running even if not owned any more by praise? Who was owning them then? Praise