Higher education systems featuring intense competition have developed world-class universities, capable of attracting top professors and students and considerable public-private funding. This does not occur in non-competitive systems, where highly talented faculty and students are dispersed across all institutions. In such systems, the authors propose the budding of spin-off universities, staffed by the migration of top scientists from the entire public research system. This article illustrates the proposal through an example: the spin-off of a new university in Rome, Italy staffed with the best professors from the three current public city universities. Such a faculty would offer top national research productivity, a magnet to attract the other critical ingredients of a world-class university: talented students, abundant resources and visionary governance.