How to implement single signin and signup for multiple Sub-domains Php

What is the best way to enable different apps in different sub-domain use one authentication system in such a way that: 1) Registration happens just once in on of the app and the rest would use it? 2) Sign in happens just one and user would be automatically logged in when he/she visits any of the other apps? 3) Secured part of any of the app would still be available after browser that was closed without logging out is reopened?