This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
because a graphics context is usually quite unique to a machine/address space/device and serialising it over the wire makes absolutely no sense to the receiving context.
Basically, wanting to draw onto a remote graphics context is a very very bad idea. If you are wanting to say remotely control/cause to draw things between some client and server then you are better off looking at some form of protocol/messaging system between the two entities. This would abstract away the physical devices and provide adequate seperation.