Is there a complete cortico-cortical connectivity map based on a useful partitioning of the cortex?
Yes-- you may be very interested in the Human Connectome Project (also here), whose goal is to map human brain connectivity.

One of the primary tools used to map functional and anatomical connections is diffusion tensor imaging (DTI). Unlike the more often used T2-weighted images, DTI allows researchers to image white matter tracts directly.

The data from the HCP is available for free to researchers, but you need to apply for access. See their website for details.