Vincas Grigas et al. have published "'Just Google It'—The Scope of Freely Available Information Sources for Doctoral Thesis Writing" in Information Research.
Here's an excerpt:
Library collections and subscribed databases could cover up to 80 per cent of all information resources used in doctoral theses. Among the most significant findings to emerge from this study is the fact that on average more than half (57 per cent) of all utilised information resources were freely available or were accessed without library support. We may presume that the library as a direct intermediator for information users is potentially important and irreplaceable only in four out of ten attempts of PhD students to seek information.