public ChildAccountsContactsController(ApexPages.StandardController controller){
    Id accId = controller.getId();
    Set<Id> allChildAccount = getAllChildAccountIds(accId);

    allContactNames = new List<Contact>();
    allContactNames = [Select Id, Name, Account.Name, Account.Parent.Name, Email, Phone from Contact where AccountId in :allChildAccount];
}

 private Set<Id> getAllChildAccountIds(Id parentAccountId){
    Set<Id> AccountIdSet = new Set<Id>();
    AccountIdSet.add(parentAccountId);
    Boolean check=true;
    do
    {
        List<Account> accIds = [select Id from Account where ParentId in:AccountIdSet And Id not in:AccountIdSet];
        if(accIds != null && accIds.size() > 0){
            for(Integer i=0; i<accIds.size(); i++){
                AccountIdSet.add(accIds[i].Id);
            }
        }
        else
            check = false;
    }while(check);
    return AccountIdSet;
}