This work set out to establish the response equations for hepatic blood flows in sheep and the contribution of hepatic arterial flow to hepatic venous blood flow due to changes in intake levels at constant diet composition. The FLORA (FLuxes across Organs and tissues in Ruminant Animals) database was used, and meta-analysis performed. The meta-analysis involved selection of published papers, identification of studies, description and coding of the selected dataset and statistical analysis using a covariance model. Meta-analyses were carried out using a within-study approach. To ensure absence of bias, the analysis incorporated interfering variables and factors studied in between-study comparisons. Variables concerned diet composition; qualitative factors concerned the physiological state of the animals and the methods used to measure blood flow. The results obtained showed that hepatic blood flows were positively related to intake in sheep. The magnitude of the response (as indicated by the slope) varied with the level of intake and the blood vessel (portal, hepatic venous or arterial). Nine linear relationships were established for the portal, hepatic venous and arterial blood flows as a function of dry matter intake (DMI) with below- and above-maintenance levels considered separately. Data obtained at below- and above-maintenance levels were considered together and four quadratic relationships were established for hepatic blood flows as a function of DMI. These relationships expressed a strong effect of intake on hepatic blood flows. The contribution of hepatic arterial to hepatic venous blood flow averaged 18.2%, with a wide variability. It did not vary significantly with level of intake. Although in between-study comparisons the arterial/venous blood flow was positively influenced by the organic matter digestibility of the diet, the relationships we obtained were robust. They can be used in models of net hepatic nutrient fluxes to predict variations and absolute values of hepatic blood flows from variations and absolute values of DMI.