One mutiple UUID file for identification through x browsers

PLEASE READ BEFORE BID- ALL BID WILL BE DELETED IF YOU HAVE NOT READ THIS TEXT We want a single file/cookie or other, be placed on users device - when she have accept terms and cookies/etc - to have file/cookie etc, to be stored local storage on her device - AFTER the user got their account registered. 1) So if the user registration is done through a Chrome browser 2) Then the user open up another browser, say for example Firefox or Internet explorer and visit the same site again, The our (your ) script on our site runs to check if this file / cookie etc exist on the user device. IF not then user can register a new account. IF user have the file, then our pages open up/login into their account to be accessed again on the different browser.