The germ disc in a bird (a disc because its a chordate) is a mystery to me. The ovum (yolk) is a huge mass of nutrients. It then gets impregnated. Then, what? What does the initial cell divisions look like (they can't be symmetrical since yolk is clearly pushed to one end of the whole thing. )
This is covered well in almost any text that talks of early embryonic development in birds. Basically, the cleavage divisions look roughly symmetrical if you look end-on from the animal pole. But, as mentioned in the question, the process is quite asymmetrical in profile, with the blastoderm being at one end and the huge yolk occupying the other.
The yolk later gets invested by a layer of cells (the splanchnopleure) to form the yolk sac while the blastoderm forms the embryo proper.
You could see this page for more details. (Not just this page, this site in general is an excellent resource for learning embryology.)
The question is based on the false belief that the ovum contains the yolk as a single cell. This is a belief that is very common, and often spread in the literature. Grau and Wilson said in 1963 in Avian Oogenesis and Yolk Deposition: The yolk of the hen's egg is often given as an example of a huge cell containing a food supply for the developing chick embryo. Current views hold that oocytes grow by removing nutrients from the blood and the follicle cells which surround them. Thus yolk deposition is thought of as primarily an intracellular phenomenon. We believe that this viewpoint is inadequate, and wish to propose the following alternative hypothesis.
Of course, if the yolk is not inside the ovum, then there is no mystery to the early cell divisions.