As I use a laptop, if some one is uploading from me and I switch off my computer, do they automatically transfer to another server or do they wait untill I am back online again, I guess my question is how does this work?

If you're running as an ultrapeer I'm not sure.

If they are dwnlding from you then if they are also dwnlding from others, they will continue those dwnlds from the others. If you're the only one with the file then they will be sort of stuck until you come online again.

That's why occasionally re-searching can find fresh sources b/c people do go offline. But a person who has their set up properly configured may not even need to search for sources everytime they open LW. After LW settles down, some of their dwnlds will continue by themselves. And whilst people are uplding from them, it helps them obtain multiple sources for their dwnlds.