What I was told was that you are selected for one of nine branches:
Naval Operations (MARS)
Naval Engineering (Marine Systems or Combat Systems Engineer)
Army Operations (Combat Arms: Infantry, Artillery, and Armour)
Army Engineering (Electrical and Mechanical Engineer and Combat Engineer (I think)
Air Operations (Pilot, Navigator, Air Controller)
Air Engineering (Airfield Engineer)
Support in all three elements (Nursing, Logician, Military Police, maybe Intelligence)
Don't quote me on the above, but I believe that's correct. Anyway lets say you apply first for Air Logician, second for Electrical and Mechanical Engineer, and Third for MARS. They will then review you and offer you a position in either Air Support, Army Engineering, or Naval Operations respectively. If you accept, for example, Army Engineering, at the end of your first year they will sit you down and based on how competitive you are either offer you your preferred trade (Electrical and Mechanical Engineer), or, if you are not deemed competitive, another trade from that branch (in this case, Combat Engineer) and then you will be trade designated and good-to-go for trade training. The only exception to this is MARS as it is the only trade in the Naval Operations Branch.
NOTE: From what I was told, if you want a trade outside of your branch you have to tell someone and get the paperwork going. If you do not get your intended trade at then end of first year you will only be given a choice of trades within the same branch no matter what your choices were when you applied.
Hope that helps.