Before revision:  The share of authors with multiple affiliations increased substantially over the past two decades and particularly since the mid-2000s. The increase is particularly pronounced in countries whose funding structures became more competitive. The rise of multiple affiliations points to fundamental changes in URLanisation of science and challenges our measurements of where scientific activity takes place .
After revision:  The share of authors with multiple affiliations increased from 6.7\% to 11.8\% since 1996. The growth of multiple affiliations is prevalent in all disciplines and it is stronger in high impact journals. About 60\% of multiple affiliations involve institutions from within the academic sector and international co-affiliations often involve institutions from the United States, Germany and the United Kingdom as well as institutions in neighboring countries. We discuss potential causes and show that the timing of the rise in multiple affiliations can be linked to the introduction of more competitive funding structures such as 'excellence initiatives' in a number of countries. We discuss implications for science and science policy .