We present the correlations between stellar mass, star formation rate (SFR) and [NII]/Ha flux ratio as indicator of gas-phase metallicity for a sample of 222 galaxies at 0.8 < z < 2.6 and log(M*/Msun)=9.0-11.5 from the LUCI, SINS/zC-SINF and KMOS3D surveys. This sample provides a unique analysis of the mass-metallicity relation (MZR) over an extended redshift range using consistent data analysis techniques and strong-line metallicity indicator. We find a constant slope at the low-mass end of the relation and can fully describe its redshift evolution through the evolution of the characteristic turnover mass where the relation begins to flatten at the asymptotic metallicity. At fixed mass and redshift, our data do not show a correlation between the [NII]/Ha ratio and SFR, which disagrees with the 0.2-0.3dex offset in [NII]/Ha predicted by the fundamental relation between stellar mass, SFR and metallicity discussed in recent literature. However, the overall evolution towards lower [NII]/Ha at earlier times does broadly agree with these predictions.