Where on a cellphone does the electromagnetic radiation(radio frequencies) come from? the antennae or the transmitter?
The majority comes from the antenna.  However, no system is 100% perfect, and there will always be some leakage from other portions of the circuit.

Also, the rest of the phone will be generating high frequency (RF) EMI fields.  The CPU in the phone typically runs at 1GHz or so, and the various peripherals all use clocked (serial or parallel) high frequency (MHz) signals, all of which radiate RF EM fields.  Yes, the phone has to be designed to limit the amount radiated to pass its certifications, but that doesn't cut out 100% of all EMI.