A homogeneous transit-timing-variation investigation of all TESS systems with a confirmed single-transiting planet

Context. Transit-timing variations (TTVs) are a powerful tool for detecting unseen companions in systems with known transiting exoplanets and for characterising their masses and orbital properties. Large-scale and homogeneous TTV analyses represent a valuable method to complement the demographics of planetary systems and understand the role of dynamical interactions. Aims. We present the results of a systematic TTV analysis of 423 systems covering ∼16000 transits, each with a single transiting planet first discovered by the NASA TESS mission and then confirmed or validated by follow-up studies. The primary aim of this survey is to identify the most promising candidates for dynamically active systems that warrant further investigation. Methods. Our analysis was performed in a two-stage pipeline. In the first stage, precise measurements of individual transit times are extracted from the TESS light curves for each system in a homogeneous way. In the second stage, we applied a two-tiered decision framework to classify candidates by analysing the resulting transit variations. Based on excess timing scatter (χmod2) and the difference in Bayesian information criterion (ΔBIC) of periodic models over linear ones, the TTVs were classified as significant, marginal, or non-detections. Results. We find 11 systems with significant TTVs, five of which were announced in previous works, and ten more systems with marginal evidence in our sample. We present three-panel diagnostic plots for all the candidates, showing phase-folded light curves, the transit variations over time, and the same variations folded on the recovered TTV period. A comprehensive summary table detailing the fitted parameters and TTV significance for the entire survey sample is also provided. Conclusions. This survey constitutes the largest homogeneous TTV analysis of TESS systems to date. We provide the community with updated ephemerides and a catalogue of high-quality TTV candidates, enabling targeted follow-up observations and detailed dynamical modelling to uncover the nature of unseen companions and study system architectures.