Colostrum provides newborn piglets with energy, immunoglobulins and growth, thereby playing an essential role in piglet survival. However, colostrum yield and composition are highly variable among sows. Some of the factors involved in this variability have been identified. The aim of the study was to confirm previous findings on a large number of animals and to investigate other potential factors of variation, such as the process of farrowing and the morphological changes of the mammary epithelium that occur during the 24 h postpartum. The experiment was conducted on 16 Large White (LW) and 56 Landrace (LR) × Large White (LR × LW) crossbred sows of mixed parities and their litters. Most farrowings were induced at 113 days of gestation and all farrowings were attended. Each piglet was weighed at birth and 24 h after farrowing started (t24). Colostrum ingestion by individual piglets was estimated using piglet weight gains from birth to t24. Colostrum production by sows was estimated by summing up colostrum intakes by each piglet of the litter. Colostrum was collected at the onset of farrowing (t0) and at t24 to determine concentrations of immunoglobulins G (IgG), Na and K. Analyses of correlations and multiple regressions were performed to identify the variables involved in variation of colostrum yield and IgG concentrations. Colostrum yield was not related to litter size and weight (P > 0.1). It was negatively correlated with the number of stillborn piglets (r = −0.33, P = 0.005) and within-litter variation of piglet birth weight (r = −0.24, P = 0.04). It was not related to the Na/K ratio in the colostrum, which is an indicator of the integrity of the mammary epithelium. When sows were categorised according to their level of colostrum yield, sows that produced a low yield of colostrum had more stillborn piglets at birth than the other sows (P < 0.05) and tended to have a longer birth interval during the early process of parturition (P < 0.1). At t24, concentrations of IgG in the colostrum were positively correlated with the Na/K ratio in the colostrum (r = 0.53, P < 0.001), which indicates the concomitance of the cessation of IgG transfer to the colostrum and the changes in the morphology of the mammary epithelium. This study points out the need for future research on the role of the hormones involved in both the process of parturition and lactogenesis in the relationship between stillbirth, process of parturition and colostrum production.