Context. In the centre of pre-stellar cores, the deuterium fractionation is enhanced due to the cold temperatures and high densities. Therefore, the chemistry of deuterated molecules can be used to probe the evolution and the kinematics in the earliest stages of star formation. Aims. We analyse emission maps of cyclopropenylidene, c-C3H2, to study the distribution of the deuteration throughout the prototypical pre-stellar core L1544. Methods. We used single-dish observations of c-C3H2, c-H13CC2H, c-C3HD, and c-C3D2 towards the pre-stellar core L1544, performed at the IRAM 30 m telescope. We derived the column density and deuterium fraction maps, and compared these observations with non-local thermodynamic equilibrium radiative transfer simulations. Results. The highest deuterium fractions are found close to the dust peak at the centre of L1544, where the increased abundance of H2D+ ions drives the deuteration process. The peak values are N(c-C3HD)/N(c-C3H2) = 0.17 ± 0.01, N(c-C3D2)/N(c-C3H2) = 0.025 ± 0.003, and N(c-C3D2)/N(c-C3HD) = 0.16 ± 0.03, which is consistent with previous single-pointing observations. The distributions of c-C3HD and c-C3D2 indicate that the deuterated forms of c-C3H2 in fact trace the dust peak and not the c-C3H2 peak. Conclusions. The N(c-C3D2)/N(c-C3HD) map confirms that the process of deuteration is more efficient towards the centre of the core and demonstrates that carbon-chain molecules are still present at high densities. This is likely caused by an increased abundance of He+ ions destroying CO, which increases the number of carbon atoms in the gas phase.
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