This depository consists of the following numerical modelling output fields: materials (mat), viscosity (mu), temperature (t), coordinates (x, y), velocity (vx, vy) and time-step specific data required for visualization (loop) The four sets of .mat (matlab-specific format) output files correspond to the four numerical modeling experiments presented in the manuscript titled Wide versus narrow back-arc rifting: control of subduction velocity and convective back-arc thinning by Zoltán Erdős, Ritske S. Huismans and Claudio Faccenna currently under revision at the journal Tectonics. The modelling experiments were run with the 2D Arbitrary Lagrangean-Eulerean Finite Element geodynamic numerical code Fantom. For ease-of-use we provide a simple matlab-script specifically designed to read-in and visualize the output data files.