The growth of oceanic plates at mid-ocean ridges, crustal accretion, occurs by a combination of magmatic and tectonic processes. Magmatic processes along ridges spreading at fast, intermediate and slow rates, continually add volcanic material to a centrally located spreading axis. This creates a narrow band of young volcanic rocks. However, at ridges spreading at ultraslow rates, diminished volcanism allows entire blocks of mantle to spread on the sea floor by tectonic processes. Remote imaging has advanced our observational understanding of crustal accretion, but temporal constraints are required to quantitatively understand ultraslow-spreading ridge construction. Here, we use U-series eruption ages of volcanic rocks collected from the ultraslow-spreading Southwest Indian Ridge. Unexpectedly, we find young volcanic eruption ages that are broadly dispersed throughout the rift valley, indicating that crustal accretion of young volcanic rocks is not confined to a narrow central spreading axis. As areas of young volcanism are observed close to distinct fault surfaces, we propose that the widely dispersed volcanism may result from magma rising along faults. Our results indicate that axial-centric spreading models may not accurately describe crustal accretion at ultraslow-spreading ridges, prompting the re-evaluation of these models.