The paper is entitled "Illiberal Education: Constitutional Constraints on Homeschooling" by Kim Yuracko, a professor at Northwestern University School of Law.
As I said, more to come. If you're in the mood to read more about government education, I also recommend Gus Van Horn's analysis of Jonah Goldberg's latest article about the state of government education.
ETA: Here's the abstract (found when you scroll up on the link to download the paper):
Homeschooling in America is no longer a fringe phenomenon. Estimates indicate that well over a million children are currently being homeschooled. Although homeschoolers are a diverse group, the homeschooling movement has come to be defined and dominated by its fundamentalist Christian majority many of whom choose to homeschool in order to shield their children from secular influences and liberal values. In response to political pressure from this group states are increasingly abdicating control and oversight over homeschooling. Modern day homeschooling raises then in stark form questions about the obligations that states have toward children being raised in illiberal subgroups. Surprisingly, the legal and philosophical issues raised by homeschooling have been almost entirely ignored by scholars. This paper seeks to begin to fill this void by making a novel constitutional argument. The paper relies on federal state action doctrine and state constitution education clauses to argue that states must — not may or should — regulate homeschooling to ensure that parents provide their children with a basic minimum education and check rampant forms of sexism. This paper argues, in other words, that while there is an upper limit on how much states can constitutionally regulate and control children's education, there is a lower limit as well. There is a minimum level of regulation and oversight over children's education that states may not with constitutional impunity avoid.