As not-yet-PhD-student I hardly dare enter this forum, but, well... I was wondering, those of you having some kind of post-doc position, how closely is your work now related to you PhD theme?

I'm no postdoc, but from what I've heard it's to your advantage to turn to a subject that's perhaps related to, but not directly connected to your PhD thesis. In this way you show you have ideas of your own and do not only follow in you supervisor's footsteps.

My PhD is completely unrelated to my postdoc position in terms of specialization but within a broad same subject area.

If you do a postdoc at the dept you did a PhD then you would probably be carrying on with the same specialization.

If you change Universities then the project is obviously different. This is good if you want to diversify.