I'm going to re-use the yeast cake from a low-gravity batch to ferment a high-gravity batch.  

 - Can I just put the wort directly on it?  Does it then need to be agitated?
 - Is it worth the risk of contamination to take the whole yeast cake out, wash it, strain it, and actually re-pitch it?
 - Is there a term for this complete re-use of a yeast cake?

**UPDATE**

Pouring down on the yeast cake of the previous batch is something I do regularly and with great effect. I don't remove anything from the carboy and I only step up in gravity. This might be helped by the fact that I only use leaf hops and they do a great job latching onto break material. I also use a boil screen, so there's very little trub anyway.

Yes, you can put the wort directly in. No, it doesn't need to be agitated, but a bit of shaking for aeration doesn't hurt.

I can't speak to risk of contamination with removing and repitching slurry, but I can say that the risk of contamination with pouring down is less.