Note: If this control is a critical one, then you need also to control the conversion at a plug-in level and not only in the dialog. You may need to handle the account creation and to supress this at the pre-message stage if the prospect don't fit you business needs. For backed tools, where you only want to give to user a path, the dialog customization is enough.
The target page is located at \SFA\leads\dialogs and is called conv_lead.aspx. Here you can add your javascript logic for disabling/hidding fields in page or whatever actions you want.
For handling the options from convert lead dialog, based on some lead parameters, you have 2 options:
1. one is to modify the lead form page (SFA\leads\edit.aspx) and give the wanted parameters as an argument for the dialog (search in convertLead function where to do this)
2. the secind methid is ti catch the output selection from the lead convert dialog and handle it on save method of the lead form.(http://vinothmscrm.blogspot.com/2010/10/validaterestrict-convert-lead_03.html)