charger - Charge controller for Li-ion or Li-Polymer battery

I am trying to work out the good charger for Mobile phones, which can serve as good performer for various smart phones out there in market these days & mostly using Li-ion battery. Charging has 4 stages -- "the initial trickle-charging, then constant current charging, then constant voltage charging & finaly Top-up charge" -- all this is controlled & monitored by a control circuit/IC of charger. So, my concern is if such circuit/module/IC is already there in Mobile phones & taking care of all protections to battery/phone including overheating during charge OR The charger designer have to incorporate these circuits in Charger itself? If former case, that means we just need to make a charging source giving ample current & 4.75V-5.25V voltage, like a high-powered USB output port would gives. My feeling is such stages-wise charging & control/monitor circuitry is already within the phone set, i just want to reconfirm.