How cooperative or competitive is the mining process? As each miner works out which nonces it has tried, does it notify the network so that energy isn't wasted on re-processing the same thing by each node? Or is it totally competitive with everyone for themselves?
Miners that aren't cooperating will never replicate work because they each want to get a different block as the next official block. If nothing else, the account the mining fee is paid to will be different. (And this ripples up to the header.)

For miners that are cooperating, work units are assigned by the mining pool. The pool will typically embed a different coinbase in the work units it assigns to each miner. When a miner finishes processing a work unit, it requests a new work unit (with a new coinbase) from the mining pool.

So there should never be any replicated work.