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The astrometric sample of Gaia allows us to study the outermost Galactic disc, the halo and their interface. It is precisely at the very edge of the disc where the effects of external perturbations are expected to be the most noticeable. Our goal is to detect the kinematic substructure present in the halo and at the edge of the Milky Way (MW) disc, and provide observational constraints on their phase-space distribution. We download, one HEALpix at a time, the proper motion histogram of distant stars, to which we apply a Wavelet Transformation to reveal the significant overdensities. We then analyse the large coherent structures that appear in the sky. We reveal a sharp yet complex anticentre dominated by Monoceros (MNC) and the Anticentre Stream (ACS) in the north, which we find with an intensity comparable to the Magellanic clouds and the Sagittarius stream, and by MNC south and TriAnd at negative latitudes. Our method allows us to perform a morphological analysis of MNC and ACS, both spanning more than 100$^\circ$ in longitude, and to provide a high purity sample of giants with which we track MNC down to latitudes as low as $\sim$5$^\circ$. Their colour-magnitude diagram is consistent with extended structures at a distance of $\sim$10-11 kpc originated in the disc, with a very low ratio of RR Lyrae over M giants, and kinematics compatible with the rotation curve at those distances or only slightly slower. We present a precise characterisation of MNC and ACS, two previously known structures that our method reveals naturally, allowing us to detect them without limiting ourselves to a particular stellar type and, for the first time, using only kinematics. Our results allow future studies to model their chemo-dynamics and evolution, thus constraining some of the most influential processes that shaped the MW.