I realise that the answer to this question varies greatly between department and universities but I would like to get some estimates from somebody within the field since I myself has absolutely no idea. When I apply for a PhD position, can I expect to compete with a handful of other persons or can there be hundreds of applications sent?
The PhD market in CS in Austria is very much a buyers market. I know from at least two professors (both are very well known in their respective fields; one of them is a real "big name" in algorithms) that they have problems finding (reasonable good and motivated) PhD students. As a well doing Master's student (not a genius, they tend to go to the US or UK), I was offered several PhD positions.