How much of a grad-school dissertation fellowship should I personally keep? I've recently been awarded a graduate school dissertation fellowship which (unlike many other fellowships) is awarded directly to me personally rather than to my institution. Normally, when fellowships are awarded through my institution, the amount of the fellowship is deducted from the stipend that my lab pays me. For example, when I received an NRSA (National Research Service Award) Fellowship, my actual take-home pay didn't change -- the NRSA money was used to cover my tuition, and to pay my stipend, instead of my lab paying it. 

In this case, since the fellowship is being awarded directly to me, I have the option of asking my PI whether I can keep some or all of it -- in effect, giving myself a raise. The fellowship is $20,000 annually, and I was considering asking for $10,000 of it, and allowing the other $10,000 to be applied against my tuition. Does that sound reasonable to you? I haven't heard of other people doing it, so I'm not really sure what the rules around this are. I also don't want to annoy my boss. 

I'm a graduate student in biology.
If money is awarded to you personally as a gift, you may do what ever you want with all of it.  You should consult with the awarding agency to determine if the award is a gift or if it comes with contractual obligations.