Adjustment for prognostic covariates increases the statistical power of randomized trials. The factors influencing the increase of power are well-known for trials with continuous outcomes. Here, we study which factors influence power and sample size requirements in time-to-event trials. We consider both parametric simulations and simulations derived from the Cancer Genome Atlas (TCGA) cohort of hepatocellular carcinoma (HCC) patients to assess how sample size requirements are reduced with covariate adjustment. Simulations demonstrate that the benefit of covariate adjustment increases with the prognostic performance of the adjustment covariate (C-index) and with the cumulative incidence of the event in the trial. For a covariate that has an intermediate prognostic performance (C-index=0.65), the reduction of sample size varies from 3.1% when cumulative incidence is of 10% to 29.1% when the cumulative incidence is of 90%. Broadening eligibility criteria usually reduces statistical power while our simulations show that it can be maintained with adequate covariate adjustment. In a simulation of adjuvant trials in HCC, we find that the number of patients screened for eligibility can be divided by 2.4 when broadening eligibility criteria. Last, we find that the Cox-Snell\documentclass[12pt]{minimal}
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				\begin{document}$${R}_{\mathsf{C}\mathsf{S}}^{2}$$\end{document}RCS2is a conservative estimation of the reduction in sample size requirements provided by covariate adjustment. Overall, more systematic adjustment for prognostic covariates leads to more efficient and inclusive clinical trials especially when cumulative incidence is large as in metastatic and advanced cancers. Code and results are available athttps://github.com/owkin/CovadjustSim.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13063-023-07375-0.