Laptops either ship with video cards pre-installed or rely on "integrated" graphics - if you laptop is running integrated graphics then there is no upgrade option.
If however you have an existing ATI graphics card already installed, then there is a small possibility to upgrade. However I doubt that you will find a replacement, and secondly i doubt swapping video cards on a laptop for something bigger / better is going to be easy.
Will involve ebay for motherboards that have a 3870 on them and a lot of very small soldering. Then calling up the company that made your laptop and complaining that the 3870 you just installed isn't working.
I understand your frustration in finding an upgrade for your laptop's video card. I also have the wonderful experience of trying to find upgrades, while mine is totally upgradeable with an empty graphic card space I find my self having to go to the computer company where i bought my computer to order said upgrades, in my case Alienware. While this works it can be very expensive. Why should i have to pay $500 per 1gb of graphics, and yes i can have 2 of them in a laptop.