Deuterium fractionation is dependent on various physical and chemical parameters. Thus, the formation location and thermal history of material in the solar system is often studied by measuring its D/H ratio. This requires knowledge about the deuteration processes operating during the planet formation era. We aim to study these processes by radially resolving the DCN/HCN (at 0.3 resolution) and N$_2$D$^+$/N$_2$H$^+$ (0.3 to 0.9) column density ratios toward the five protoplanetary disks observed by the Molecules with ALMA at Planet-forming scales (MAPS) Large Program. DCN is detected in all five sources, with one newly reported detection. N$_2$D$^+$ is detected in four sources, two of which are newly reported detections. We derive column density profiles that allow us to study the spatial variation of the DCN/HCN and N$_2$D$^+$/N$_2$H$^+$ ratios at high resolution. DCN/HCN varies considerably for different parts of the disks, ranging from $10^{-3}$ to $10^{-1}$. In particular, the inner disk regions generally show significantly lower HCN deuteration compared with the outer disk. In addition, our analysis confirms that two deuterium fractionation channels are active, which can alter the D/H ratio within the pool of organic molecules. N$_2$D$^+$ is found in the cold outer regions beyond $sim$50 au, with N$_2$D$^+$/N$_2$H$^+$ ranging between $10^{-2}$ and 1 across the disk sample. This is consistent with the theoretical expectation that N$_2$H$^+$ deuteration proceeds via the low-temperature channel only. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.
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