Mojo Helpdesk requires that one form is published at all times. You are able to change the default form using the 'set as default' flag in the form list.
The default form will be the one that is used by all incoming tickets created by email.
Tickets created by email will always use the default form but you are able to change the form for those tickets once the ticket is created. You can do this by clicking the grey 'edit' button on any ticket.