Yes, you can install and activate the same copy of TurboTax on three different computers. However, you can download it on one computer at a time. So, if you are sharing the software, you need to download it on one computer, finish your returns, then uninstall it before you can download it on the second one
Note: When you activate the same copy of TurboTax on multiple computers, the maximum limit for the total number of tax returns that apply to your copy of TurboTax gets shared among your installations.
For example, if your TurboTax includes 8 paid returns and you already filed 3 returns from one computer and 2 from another, you can only file 3 more returns using the third computer (that is, 8 – (3+2) = 3).