Human capital is a funky capital stock. In our diverse world, kids have a vector of cognitive and non-cognitive endowments. As time passes, investments in own time, parental time and market inputs are made to increment the elements of these vectors. These investments are actively made by investors (the parents and the person him/herself) who are aware of the market rate of return to these various attributes. Human capital theory sought to recast investment in people as similar to any theory of investment with the exception that human capital is embodied in a living person and thus can't be transferred at death or sold except it can be rented in labor markets. Risk neutral investors will undertake all projects with an expected present discounted value that they can finance.
Early on, Gary Becker and others recognized the key role of capital constraints in limiting access to "good projects". If you can't pay Harvard's tuition and it doesn't offer you financial aid, then you won't go even though Harvard might be a great treatment for you.
To see some strange discussion about human capital in Slate read this.
In Piketty's race between "r" and "g", I don't see how he incorporates the non-linear returns to human capital. One way for "g" to rise faster than "r" is to identify binding capital constraints that limit productive human capital investments. Incomplete capital markets limit the ability of those who would greatly benefit from human capital investment from contracting with the "capitalists" to borrow from them. If such trades could occur (and depending on the terms of the trade and on how aggregate growth increases as a function of our human capital stock), then it is possible that the economy would grow at a rate (g) greater than the market rate of interest (r).
For good theorists, is Piketty writing down a complete markets model or one in which there are incomplete markets for skill formation? Without engaging in his global wealth tax are there other markets that if they were introduced would lead to g > r? My intuition is that market structure matters and over time transaction costs are falling so the world's economy in the limit approaches the Arrow-Debreu ideal.