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It is often stated that star clusters are the fundamental units of starformation and that most (if not all) stars form in dense stellar clusters. Inthis monolithic formation scenario, low density OB associations are formed fromthe expansion of gravitationally bound clusters following gas expulsion due tostellar feedback. $N$-body simulations of this process show that OBassociations formed this way retain signs of expansion and elevated radialanisotropy over tens of Myr. However, recent theoretical and observationalstudies suggest that star formation is a hierarchical process, following thefractal nature of natal molecular clouds and allowing the formation oflarge-scale associations in-situ. We distinguish between these two scenarios bycharacterising the kinematics of OB associations using the Tycho-$Gaia$Astrometric Solution catalogue. To this end, we quantify four key kinematicdiagnostics: the number ratio of stars with positive radial velocities to thosewith negative radial velocities, the median radial velocity, the median radialvelocity normalised by the tangential velocity, and the radial anisotropyparameter. Each quantity presents a useful diagnostic of whether theassociation was more compact in the past. We compare these diagnostics tomodels representing random motion and the expanding products of monolithiccluster formation. None of these diagnostics show evidence of expansion, eitherfrom a single cluster or multiple clusters, and the observed kinematics arebetter represented by a random velocity distribution. This result favours thehierarchical star formation model in which a minority of stars forms in boundclusters and large-scale, hierarchically-structured associations are formedin-situ.

Not all stars form in clusters - measuring the kinematics of OB associations with $Gaia$