I want to open a new account and transfer some forms from one to another. How do I do that?

You can signup and create a new account here - https://www.jotform.com/signup/ 

After you create a new account, we can move your forms. You will need to provide us the username of the new account and links of the forms you want to move. 

How to transfer or share forms and data with another account

Please note that the request for moving the forms has to be made from the account on which the forms are located. You can post the request for moving the forms on this thread.