... holes

Appendix is only available in electronic form at http://www.aanda.org

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... limit

Note that it would be incorrect to attempt to calculate the evolution in $\rho_{\rm BH}(z)$ by integrating $\langle {\rm d}\log M/{\rm d}t\rangle$: in hierarchical growth, mergers are important and evolution of the mass function is described by the Press-Schechter function.

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