In living organisms, the same enzyme catalyses the degradation of thousands of different mRNAs, but the possible influence of competing substrates has been largely ignored so far. We develop a simple mechanistic model of the coupled degradation of all cell mRNAs using the total quasi-steady-state approximation of the Michaelis–Menten framework. Numerical simulations of the model using carefully chosen parameters and analyses of rate sensitivity coefficients show how substrate competition alters mRNA decay. The model predictions reproduce and explain a number of experimental observations on mRNA decay following transcription arrest, such as delays before the onset of degradation, the occurrence of variable degradation profiles with increased non linearities and the negative correlation between mRNA half-life and concentration. The competition acts at different levels, through the initial concentration of cell mRNAs and by modifying the enzyme affinity for its targets. The consequence is a global slow down of mRNA decay due to enzyme titration and the amplification of its apparent affinity. Competition happens to stabilize weakly affine mRNAs and to destabilize the most affine ones. We believe that this mechanistic model is an interesting alternative to the exponential models commonly used for the determination of mRNA half-lives. It allows analysing regulatory mechanisms of mRNA degradation and its predictions are directly comparable to experimental data.