We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspired by the proof of scaling relations for Bernoulli percolation by Kesten . Along the way, we show an annealed quasi-multiplicativity property by relying on the quenched box-crossing property proved by Ahlberg, Griffiths, Morris and Tassion . Intermediate results also include the study of quenched and annealed notions of pivotal events and the extension of the quenched box-crossing property of  to the near-critical regime.
"Annealed scaling relations for Voronoi percolation." Electron. J. Probab. 24 1 - 71, 2019. https://doi.org/10.1214/19-EJP293