Abstract The preservation and accretion rates of fluvial meander-belt deposits appear to vary with the time over which they are evaluated, but the drivers of this effect are not fully understood. Using channel trajectories tracking the temporal evolution of meandering rivers, constrained with data on past river planforms, a numerical model is used to simulate planform evolutions of meander-belt reaches that underwent different types of meander transformation behaviours and bend cutoffs. Sediment preservation and bar accretion rates are quantified for three hierarchies of depositional products: (i) accretion stages reflecting intervals of bend migration by a certain meander-transformation style, (ii) meander-belt segments encompassing multiple stages but no bend cutoffs and (iii) meander-belt segments that experienced one or multiple cutoffs. Results show that distinct power-law relationships between the accretion rate and the time of sedimentation exist for river systems of different magnitudes in scale. Within each order of magnitude in river-system size, a single power-law relationship fails to effectively capture all depositional hierarchies. Sediment preservation varies with the time over which it is computed, but systematic variations in accretion rates with time primarily portray an apparent dependency of river migration rates on time: these variations largely reflect the temporal resolution and timespan of the modelled examples, highlighting an inherent issue affecting studies of river evolutions.