I believe Ichigo's hollow first came around while he was training under Urahara to be come a shinigami. If you remember, he had to make it out of some big pit before the chain on his chest destroyed itself. If he did not make it out, he would become a hollow, but if he did, he would once again become a shingami. He made it out just as the chain was destroyed. In theory, if he made it out just as the chain was destroyed, he would have become a combination between a shinigami and a hollow, now known as a Vizard. Nameless(The name given to Ichigo's hollow by members on another forum. It makes things more convenient), seems to be repressed by Ichigo's consciousness, whereas the shinigami seems to be mutual with Ichigo's consciousness. Nameless appears to be all of the emotions and power that Ichigo holds back, or has the potential to have. Nameless also seems to have a consciousness of his own, similar to something along the lines of Multiple Personality Disorder.
We still do not know enough about Ichigo's hollow to draw any conclusions, other than the fact that it is stronger than Ichigo as a shinigami. Anything we can come up with is just theoretical.