What you're talking about boils down to the basic maths of pagerank.
1000 links to one pumper page = 1000 votes at pumper.
If you only have one link on the pumper site (to your money site), then the amount of vote power (link juice) transferred to your money site will be 1000 MINUS the dampening factor specified in the original pagerank papers, which was nominally about 0.7. So the money site gets 1000 * 0.7 = 700 vote power. The reason was for the dampening factor was because otherwise you could link in a circular fashion and basically increase your own pagerank to infinity.
Of course if you have more than one link on your pumper, then the outgoing voting power will be split between those links.
No one knows what the real dampening factor is, plus there are a trillion other factors at play in the transfer of linking "power" other than straight pagerank eg. anchor text, relevance, authority / trust, position on page, font size etc etc, all with varying degrees of importance.
Now if you have the same 1000 backlinks going to each of your 10 pumper sites, then obviously the outgoing link power of those 1000 backlinks is going to be split between each of those 10 pumper sites that they're linking to. From a purely mathematical perspective, it's better to have unique backlinks for each pumper.
Also note that pagerank is calculated on a PAGE BY PAGE not site by site basis, although there are other linking factors (eg. transfer of trust) that are probably calculated site by site, if you read the papers in peer reviewed journals published by current googlers.
Hope that makes sense.