Actually very hard to explain without graphics. I have notice that even chicken rice sellers chopped it differently. For home consumption, I think how we chop is not important but how we present is more important. As for commercial, it is important as it will determine the profits for the operator. I will describe very briefly with my own graphic.
From a chicken we can have 2 plates of drumstick rice - RM5.50 x 2 , 2 plates of thigh meat ( Kai yee tou )- RM4.50 x 2 , 2 plates of shoulder meat ( kai pui chek also sometimes serves as kai yee tou ) - RM4.50 x 2 , 2 plates of chicken wing rice ( kai yik ) - RM4 x 2 and from the two portions of chicken breast and the two fillets, we can divide it into 5 plates of chicken breast rice (kai huung yuk fan ) - RM4.00 x 5 . Altogether a total of 13 plates if totals up comes to RM57.00 per chicken of 2kgs. This includes the fragrant rice, the chilly sauce, the ginger sauce, the soup, rental labour which actually does not amount to much profit.

Slit the chicken at the centre of breast and then chop as near as the backbone as possible to divide the chicken into two. Cut the backbone out and discard. Take one side of the two halves and cut the wing out with a little breast attached. Cut out the drumstick but leave the thigh attached to the carcass. Divide the remaining lenghtwise separating the breast meat from the shoulder and thigh parts. Now take the breast meat and pull it apart from the bone. Dig out the fillet attached to the bone. Flatten the fillet a bit and chop. Pick up the chopped m,eat with your cleaver and place it on the plate. Slice the breast meat into to portions to thin out the meat. Chop the portion without the skin first and as before place the meat neatly on top of the fillet. Now chop the skinned portion and also place it neatly on top of the former portion.
Chop up the other half in the same way and now you have all the breast meat in the cneter of the plate. Then chop the thigh and shoulder section equally and also arrange it at the side of the breast meat. There's a bone in the center of the thigh that needs to be taken out because usually there's still blood here. Chicken is 90 percent cooked to be perfect. Do the same on the other side and then lastly chop up the wings and place it at the side. Try to arrange the chicken las where their parts should be, sometimes even the head in some festival meals. Garnish with chopped spring onions, coriader leaves and julienne red chillies.