A Research Study in Children Born Small and Who Stayed Small. Treatment is Somapacitan Once a Week Compared to Norditropin® Once a Day

Inclusion Criteria: * Pre-pubertal children, boys: 1. age between 2.5 and 11.0 years at screening. 2. testes volume below 4 ml. * Pre-pubertal children, girls: 1. age between 2.5 and 10.0 years at screening. 2. Tanner stage 1 for breast development (no palpable glandular breast tissue). * Born small for gestational age (birth length and/or weight below -2 standard deviation scores) (according to national standards). * Impaired height defined as at least 2.5 standard deviations below the mean height for chronological age and gender at screening according to the standards of Centers for Disease Control and Prevention at screening. * Impaired height velocity defined as annualized height velocity below the 50th percentile for chronological age and gender according to the standards of Prader calculated over a time span of minimum 6 months and maximum 18 months prior to screening. * No prior exposure to growth hormone therapy or Insulin-like Growth Factor-I (IGF-I) treatment. Exclusion Criteria: * Any known or suspected clinically significant abnormality likely to affect growth or the ability to evaluate growth with standing height measurements. * Children with hormonal deficiencies including suspected or confirmed growth hormone deficiency according to local practise. * Current inflammatory diseases requiring systemic corticosteroid treatment for longer than 2 consecutive weeks within the last 3 months prior to screening. * Children requiring inhaled glucocorticoid therapy at a dose of greater than 400 μg/day of inhaled budesonide or equivalents for longer than 4 consecutive weeks within the last 12 months prior to screening. * Concomitant administration of other treatments that may have an effect on growth, e.g but not limited to methylphenidate for treatment of attention deficit hyperactivity disorder. * Diagnosis of attention deficit hyperactivity disorder. * Prior history or presence of malignancy including intracranial tumours.