At what position should the center of the plate be served to a guest in a fine dining restaurant

I don't understand your question. Position on the table or at the place setting? What do you mean by center of the plate?

The position of the center of the plate in front of the person that will be eating.

I still don't understand. See if this site helps answer your question or Google "formal dining" "formal place settings" (without quote marks) --

Formal table place setting basics: dishes, silverware, glasses and more

Also look at this (and associated videos) --

http://www.youtube.com/watch?v=TN0e9moKrvs

The plate should be directly in front of the person who is going to eat off it, of course. As for the center of the plate, if the entire plate is directly in front of the person being served, the center of the plate will be - well, in the center of the plate! How fine the restaurant is has nothing to do with it - it's a practical matter.

If you're asking how food should be arranged on the plate, it doesn't matter. It's up to the chef to determine what is most appealing to the eye and practical.

I don't get this question, either... did you go to some weird restaurant where the plates were placed to the left of your elbow or under your chair or something?