Randomization of 2000 pregnant women to vitamin D of high-dose (3200 IU/day) vitamin D vs placebo on top of the recommended 400 IU/day. Supplementation begins in gestational week 24 (22-26) until 1 week after delivery. Allocation to the trial will be determined based on the pre-interventional maternal blood levels of EPA+DHA with a dried blood screening test. Women with high levels (above 4.7% of total fatty acids) will be assigned to the vitamin D RCT. Maternal blood will be used for genetic, metabolomic and proteomic profiling. A 3-year follow-up of the children with longitudinal registration of parent reported symptoms, diagnoses, medication use, and hospitalizations will be performed. The primary outcome is persistent wheeze or asthma until age 3 years, with predefined analyses of effect modification by maternal genotypes. Secondary outcomes are lower respiratory tract infections, gastrointestinal infections, croup, troublesome lung symptoms, eczema, allergy, bone fractures, developmental milestones, mental health, cognition, and growth until age 3 years. A follow-up on both primary and secondary outcomes is planned after unblinding, from age 3 to 6 years.