The objectives were to evaluate the effect of (1) supplementing concentrates to multiparous Holstein cows during the dry period on colostral and milk immunoglobulin G (IgG) concentration; and (2) feeding calves colostrum at either 5 or 10% of their body weight (BW) on passive transfer of immunity, health, and performance. Holstein multiparous cows (n = 37) were assigned to 1 of 2 nutritional treatments during an 8-wk dry period: (1) offered ad libitum grass silage only (GS) or (2) offered ad libitum access to the same grass silage plus concentrate [total mixed ration in a 75:25 dry matter (DM) ratio], providing a mean concentrate DM intake of 3.0 kg/cow per day (GSC). Both treatment groups were offered identical levels of mineral and vitamin supplementation. Calves from these cows were weighed immediately after birth and fed either 5% (5BW) or 10% (10BW) of their BW in colostrum from their own dams within 2.5 h of birth. Calves in the 10BW group received their second feed of colostrum from first-milking colostrum. Concentrate supplementation during the dry period had no effect on colostral IgG concentration, first-milking IgG yield, or fat, protein, and lactose contents. However, cows in GSC produced a greater mean milk yield over the first 8 milkings compared with cows in the GS group. Concentrate supplementation had no effect on calf BW or BW gain, serum IgG, or apparent efficiency of absorption (AEA) at 24 h after birth. However, offspring from the GSC group had fewer cases of enteritis during the first 56 d of life compared with offspring from the GS group. Calves in the 10BW group had greater mean serum IgG concentration for the first 3 d following birth; however, at 24 h after birth, we observed no treatment effect on AEA. The rate of enteritis was greater for calves in the 5BW treatment compared with 10BW. The colostrum-feeding regimen had no effect on BW gain or on the incidence of pneumonia among calf treatment groups. In conclusion, concentrate supplementation regimens offered during the dry period had a positive effect on colostrum yield, and offspring from the GSC group had a reduced rate of enteritis. Feeding 10% of BW of colostrum versus 5% of BW resulted in a greater serum IgG concentration for the first 3 d postpartum, and 10BW calves had a reduced rate of enteritis. Overall, to achieve successful passive transfer, decrease the rate of enteritis, and increase efficiency in the dairy calf, we recommend that dairy calves be fed 10% of their BW in colostrum as soon as possible after birth.