When you use Livescribe Desktop on a computer for the first time, Livescribe Desktop prompts you to log on to your Livescribe Online account. After doing so, that installation of Livescribe Desktop is authorized for (or linked to) your account.
As a Livescribe user, all your Livescribe tools link to each other using the same email address and password. This means that your smartpen registration, your Livescribe Online account, and your installations of Livescribe Desktop, all identify themselves to each other using the same email address and password.
You can use Livescribe Desktop on as many computers as you like, and you can use as many smartpens as you like. Just ensure that when you authorize Livescribe Desktop and register your smartpens, that you use the same email address and password as your Livescribe Online account.