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My 3 main, over-wintered hives (Italians) are hard at work filling all the available space, in the brood area, with nectar. The queens have no where to lay eggs. I have counted over 30 queen cells between the 3 hives. Each hive has a Med. super on them, but they don't seem interested in them.

What can I do, or what do I need to make them quit filling in the brood area with nectar???

Add another deep and checkerboard. Although, it may be too late. Once they make up their mind, they usually swarm, whether you remove the queen cells or not.Removing the Q-cells is a great way to make a hive queenless and watch it die.

I agree with Wally. I'm in the same situation. I made multiple dumb decisions this year -- a. not getting supers on soon enough to provide room for her to lay and then b: thinking I was doing the right thing and cutting out all the swarm cells (I'll show those bees not to swarm). Now I think I may have a strong queenless hive. I added another queen in a cage, we'll see if they accept her. I'm making a pact with myself to never cut out another supercedure or swarm cell again!

As far as getting them to load up in the super, I generally don't extract all my frames from the previous season, but leave a couple in the freezer. When you put your super on throw a couple frames of honey in the super. I've found that will encourage the bees to go into the super and deposit nectar there, especially if you're using a queen excluder.