Do you mean old TurboTax accounts? You do not "close" them -- nor can they be deleted. You can just abandon your old TT account. No one else has access and nothing will happen to it. You should keep a record of any account and user ID you have used to prepare a tax return so that you can access it if you ever need to. The IRS and TurboTax save returns for seven years; after that they are gone.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**