How long would a round trip to the centre of the galaxy and back take?

Given the vast size of the Milky Way, its likely that the only practical method of exploring it will be with automated probes along the lines of the Voyager spacecraft. With that assumption in mind, I have a couple of questions,

A) With today's best propulsion technology, how long would human civilisation need to last in order to welcome back a probe that had returned from a trip to the galactic centre.

B) is any there any technology that could power a probe at ~10W for the required length of time?