Per the End User License Agreement included in the EyeTV software, each EyeTV activation key allows you to install and use one copy of the Software on a single computer at a time. This License does not allow the Software to exist on more than one computer at a time, and you may not make the Software available over a network where it could be used by multiple computers at the same time. If the Software was included with a Hardware product then this License does not allow you to use the Software with another Hardware product.
Further details concerning the correct licensing of EyeTV can be found on the second screen of the EyeTV 3 Setup Assistant.