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We have followed up on our observations of the ~ 40-Myr, and still accreting, PMC Delorme 1 (AB)b. We used high-resolution spectroscopy to characterise the accretion process further by accessing the wealth of emission lines in the near-UV. With VLT/UVES, we obtained R ~ 50000 spectroscopy at 330--452 nm. After separating the emission of the companion from that of the M5 low-mass binary, we performed a detailed emission-line analysis, which included planetary accretion shock modelling. We reaffirm ongoing accretion in Delorme 1 (AB)b and report the first detections in a (super-Jovian) protoplanet of resolved hydrogen line emission in the near-UV (H-gamma, H-delta, H-epsilon, H8 and H9). We tentatively detect H11, H12, He I and Ca II H/K. The analysis strongly favours a planetary accretion shock with a line-luminosity-based accretion rate dMp/dt = 2e-8 MJ/yr. The lines are asymmetric and well described by sums of narrow and broad components with different velocity shifts. Overall line shapes are best explained by a pre-shock velocity v0 = 170+-30 km/s, implying a planetary mass Mp = 13+-5 MJ, and number densities n0 ~ 1e13/cc or n0 ~ 1e11/cc. The higher density implies a small line-emitting area of ~ 1% relative to the planetary surface. This favours magnetospheric accretion, a case potentially strengthened by the presence of blueshifted emission in the asymmetrical profiles.High-resolution spectroscopy offers the opportunity to resolve line profiles, crucial for studying the accretion process in depth. The super-Jovian protoplanet Delorme 1 (AB)b is still accreting at ~ 40 Myr. Thus, Delorme 1 belongs to the growing family of Peter Pan disc systems with protoplanetary and/or circumplanetary disc(s) far beyond the typically assumed disc lifetimes. Further observations of this benchmark companion, and its presumed disc(s), will help answer key questions about the accretion geometry in PMCs.