To some extent my answer depends on what you mean by 'wealth'? My first thought when I read your post was that Christ actually asks us to forsake all of our wealth and distribute to the poor (Luke 14:33, 12:33). He says that we cannot serve two masters, God and money (Matt 6:24). He spoke about the pearl of great price and that if people could truly perceive the treasures of the Kingdom of Heaven and the kind of wealth that Jesus was speaking about, then we would give up all our worldly wealth to acquire it. I think at this stage we would not even be thinking about worldly wealth, because we would understand its insignificance against the eternal perspective. This leaves me wondering whether we need to redefine our attitude towards wealth, before we contemplate Christ's Kingdom.
Another thought is that man created money, God didn't. If you were thinking about money with regards to 'wealth', I think money would be obsolete in Christ's economic system, because His system would be governed by the principles of the Kingdom of Heaven i.e. Christ's teachings. If everyone one is adopting these principles (Christ's teachings) then each person would be responding to the needs of others around them, and everyone will be receiving whatever they need in return, without any need for money. It is very hard to imagine Christ's physical rule on earth being mediated by a monetary system (though there may be some kind of 'gift economy' and 'resource based economy').
I'm sure He will distribute responsibility, but more responsibility may not mean more 'wealth', in a worldly sense. We only need to look at Jesus' example to realise that, spiritually speaking, the more responsibility we have, the more our lives will reflect, like Jesus, that of a servant, which (unlike a lot of other Christians may argue) would mean less (worldly) wealth, not more. He said that the greatest leader will be as a servant. I suspect until we are able to contemplate becoming nothing in the world; no wealth, no status, no nothing... just seeking to love and serve others, it will be hard for us to imagine how Christ's Kingdom will truly operate, because we will be limited by our own worldly attitudes, desires and experiences.
In summary, I think the more we can do now to put Christ's teachings (i.e. His 'system') into practice, the more we will cultivate the spiritual vision needed to understand and live out His system, that is, to build the Kingdom of Heaven on Earth.