I think I found a method. It s a grass function included inside the sextante plugin. See the screenshot. I did a test with a shapefile that looked like yours.

I think I found a method. It s a grass function included inside the sextante plugin. See the screenshot. I did a test with a shapefile that looked like yours.

More Details:

1. It is best to install QGIS Sextante Plugin. So you do not have to worry about importing/exporting to grass datasets.

2. The tool is Located in Sextante toolbox > Grass Commands > Vector > v.overlay

3. Just open the tool and use the default parameters and you get the results in a new layer