Phase II, multi-center, 3 part, staggered cohort, open-label and double blind, randomized, placebo controlled study involving 3 age-determined cohorts (Cohort 1: between 12 and 17 years old; Cohort 2: between 6 and 11 years old; Cohort 3: between 1 and 5 years old). Daily dosing with eltrombopag will begin with 5 patients in the oldest age cohort in an open label fashion, and a review of safety, pharmacokinetic and platelet count data will be performed regularly. If no safety concerns are identified after 12 weeks, 18 additional patients will be randomised to placebo or eltrombopag (2:1 randomisation). After 7 weeks of randomized treatment, all patients will receive eltrombopag in an open label fashion. The total duration of treatment with eltrombopag will be 24 weeks. If at the time of the aforementioned 12 week review of the first 5 patients no safety issues are identified, dosing will begin in the next lower age cohort with an initial group of 5 patients. The same procedure will be followed in terms of safety review and subsequent enrolment and randomisation of the additional patients. Initiation of the younger age cohort will take place once data from the previous has been evaluated. Doses will be adjusted according to platelet counts and tolerability. The study will include a review of the safety data by a Data Safety Monitoring Board.