My answer to a question on Quora :
It's theoretically possible. To make it practical you have to replace what companies do : co-ordinate and direct the actions of lots of people.
While the market can do this, negotiating a price for every bit of co-ordination is time-consuming and costly. So you need a solution to make that cheaper.
As Anon suggests, computers can help with that. (That's the line of reasoning that descends from RonaldCoase. And it's what oDesk and TheMechanicalTurk may be evolving into)
Another is to have groups of freelance-workers hire managers to tell them what to do (an unlikely eventuality).
A third option that might make it tractable is to shift a lot of what we do out of the paid economy and into a loosely accounted "gift" or "favour" economy.
The dirty secret of corporations is that they are basically a foam of capitalism enclosing (and benefiting from) huge bubbles of "gift economy". In your department you co-ordinate with and help out your colleagues not because you negotiate individually with them for every collaboration. Or even because the company pays you per task. Or because your boss micromanages your every action. (At least not in good companies.) You do it because you join a little society where the expected behaviour is to take initiative and co-operate. There's a pay-check each month, but that pay-check is just to keep you within broad parameters : coming in each day, not sabotaging the employer, not letting personal feuds become toxic.
The day-to-day co-ordination in most people's work is neither market based nor hierarchical control but spontaneous mutual support. That is what is really important (and perhaps most difficult) to continue to enable in an economy without corporations.
See also :