What exactly is making it break? Is it sticking somewhere? Sides or bottom? Make sure you run a spatula around the edges before you try taking it out and you should have parchment in the bottom of your pan.
A heating core is a metal thing that you place in the center of your batter that will radiate heat and help it bake more evenly - intended for large cakes.
How long are you letting the cakes cool before you remove them from the pans?
The easiest way to remove them in my opinion, is to cover the cake with a cake board and flip the pan over, letting the cake rest on the board. After it is COMPLETELY cooled of course. The bigger the cake, the more cooling time it needs, touch the bottom of the pan and make sure it's not warm at all before you try flipping it over. If you are one of those people who insist on taking the cake out of the pan before it is cooled completely (sigh) to cool it on a rack, then put the rack on top of the cake and do the same thing. Just don't touch the cake until you feel NO HEAT coming from it at all.
HTH
In place of a heating core many people (including myself) are using their flower nails! This way, you don't have to purchase something else and there is not a big hole/weak spot there.
To use the flower nails spray, grease, brush with bake release (whatever you do to make your pans non-stick) to the flower nail too! Place 2-4 nails in the pan upside down (the bigger the pan, the more nails you'll want to use). Pour the batter into the pan with out tipping over the nails. It works like a charm! HTH
FYI: I had to learn the hard way....that is why I am being so detailed with the usage of them! 
Those little nails aren't so cute when they are lying on the table beside your cake with cake attached!
Well maybe I need to be clear. When I bake a full sheet cake I use 2 11x15 pans. The first one is fine because I use the board to flip the cake out. It's the second one I'm having trouble with. My cake was so moist it broke in half and I had to re-bake it. When one cake is already on the board how do I successfully get the other one on??
Thanks for the heating core info. So do you pour the batter over it and if so how do you get it out once the cake is baked. Sorry, if this seems like a really, really stupid question. I just don't know.
You may want to cook one sheet at a time. The cake that turned out well, was that on the top or bottom rack in your oven? It has been my experience that when you bake cakes on the bottom rack they do not cook evenly (overly cooked on the outside and not really done on the inside). It has a lot to do with the way the heat circulates in the oven.
Is it sticking to the pan while you are flipping it or is it breaking while you are flipping it out of the pan? Is the top slighty domed? If so, are you trying to lay it on the domed side? If so, the corners will drop (gravity) because there is nothing to support them. Level the cake before taking it out of the pan. This will give you a level surface to lay it on when you flip it out. I always take another cooling rack and flip the cake again, so it is sitting on it's bottom instead of its top.
I flip my cakes out of the pan within 3 minutes of taking them out of the oven. I grease only (no flour - use CK Brand Pan Grease) and use baking strips, no flower nail and no core.
I would use another board for the second cake and slide it off the board onto the other board with the first cake.
Quick question since we are on the subject. At what size cake pans do you start using the flower nail. So far I havent delt with anything larger than a 9 x 13 and they seem to turn out fine without the nail. Just curious for when I start using larger pans. (And how many nails for which sizes???)
In addition to what indydebi said about the cake possibly being domed...when my cakes come out of the oven, I use a clean towel and cover the cake and flatten the dome down with my hands so that it is flat when you pop it out. (This also eliminates the leveling step, but I've heard some complain this changes the consistency of the cake for them. Personally, I don't mind it.)
If it still seems to stick, I smack the sides of the pan first with a rubber spatula. Then, I flip the cake pan over and beat the sides some more and then all over the bottom of the pan to loosen it up...Just make sure you use the flat part of the spatula so you don't dent your pans.
Good Luck! If all else fails...EAT THE EVIDENCE!!!! 
-Michelle
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Thanks for the heating core info. So do you pour the batter over it and if so how do you get it out once the cake is baked. Sorry, if this seems like a really, really stupid question. I just don't know.
When you have removed the cake from the pan, the bottom of the cake is now on top and you just pick it out. If you have greased it properly, it should not stick to your cake.
It's breaking while I'm fliping it out of the pan. I like the idea of using a different board. Also, my cakes generally don't have a dome. They bake evenly on top. I do use strips so I've always figuered that's why. Maybe I need to use more cake batter so that it rises higher over the pan so that I can level it better. What do you all think?
What are you putting over the cake (pan) when you are flipping it? Is the cardboad or cooling rack at least the same size as the cake? ARe you holding it securely to the pan as you flip it over? If you are doing this, I can't see how the cake would break.
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