Mechanical deformation of nanopillars displays features that are distinctly different from the bulk behavior of single crystals: Yield strength increases with decreasing size and plas- tic deformation comes together with strain bursts or/and stress drops (depending on load- ing conditions) with a very strong sensitivity of the stochasticity character on material preparation and conditions. The character of the phenomenon is standing as a paradox: While these bursts resemble the universal, widely independent of material conditions, noise heard in bulk crystals using acoustic emission techniques, they emerge primarily with decreasing size and increasing strength in nanopillars. In this paper, we present a re- alistic but minimal discrete dislocation plasticity model for the elasto-plastic deformation of nanopillars that is consistent with the main experimental observations of nano pillar compression experiments and provides a clear insight to this paradox. With increasing sample size, the model naturally transitions between the typical progressive behavior of nanopillars to a behavior that resembles evidence for bulk mesoscale plasticity. The com- bination of consistent strengthening, large flow stress fluctuations and critical avalanches is only observed in the depinning regime where obstacles are much stronger than disloca- tion sources; in contrast, when dislocation source strength becomes comparable to obsta- cle barriers, then yield strength size effects are absent but plasticity avalanche dynamics is strongly universal, across sample width and aspect-ratio scales. Finally, we elucidate the mechanism that leads to the connection between depinning and size effects in our model dislocation dynamics. In this way, our model builds a way towards unifying statistical as- pects of mechanical deformation across scales.