The answer, for BGA chips, is: Don’t. Clean up the pads on the board, displace the factory lead free solder with leaded, but don't try to build balls on the board. Leave very little.
With a stencil and solder paste you’ll have quite good control over the size of the balls that go on the chip. You won't achieve anywhere near the same concistancy if trying to build balls or large mounds on the board “manually”, and you’ll run a high risk of undersized ones not making contact and large ones lifting the whole chip so many others don't make contact.
Don’t prebuild balls or mounds on the board pads of other types of chips (non-BGA) either, if only working with an iron, or your chip won't seat on the board because you can only melt one joint (or side) at a time.
If you (or anyone else starting out) see this: Don't cheap out on super cheap stencils. They can be a real headache to work with, and the last thing you need starting out is fighting your tools while learning. You don't need to go all out with 3d stencils, but stencils with little studs on one side that aligns the chip correctly with the stencil, is a godsent. Also get stencils eith rounded square holes. These release the chip/balls much easier after melting the paste. If buying larger multi-chip stencils, or single-chip stencils for large chips, you may want to consider direct-heat stencils. These have slots cut into them along the sides of the chip footprint, that drastically reduces stencil warping when heating.
As others have mentioned, a BC1 tip is not really your friend for working on these board pads like that, there's just too little thermal mass in the tip, and iphone/ipad/mac boards will instantly soak it up, making it too cold. You really wanna be using the biggest tip and contact area you can safely and precisely navigate in the area you're working. This goes for soldering in general, not just this particular example. If cleaning up and prepping pads for BGA soldering, I would suggest you get yourself a BCM2 tip. Its also awesome for drag soldering and nipping out solder bridges. It has a small indent in the tip, which will hold or wick a bit of solder. Some also use K/KN tips for pad work. You can get fairly good knock-offs of T12 tips (identical to T15, just different model name for diffeeent markets) for just 3-4 bucks a pop if buying 3-4 or more at a time. They're probably 80-85% there, so its an affordable way of trying out different types to find which types work best for you, your work snd technique. Then you can get the real deal once you got it narrowed down.
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