Registering the stock, whether you invest directly via a no-load stock plan or go through the broker to get the first share, is an important consideration when starting a child in the plan. You could merely open up an account in your own name. In this way, you control the plan. However, disadvantages to this approach are that you will be taxed on income earned in the plan at your tax rate. Funds in the account are in the minor's name and social security number and are considered to be owned by the minor.
Dividends paid on the account are taxable, most likely at a preferred tax rate.
The adult custodian is responsible for the account until the minor reaches the age of majority. Any withdrawals from the account are payable to the custodian on the minor's behalf until that time. Parental control is lost at the age of majority. Hopefully, by the time a child reaches 18, the principles of investing are so ingrained that he or she would be reluctant to squander funds that took so long to accumulate. Nevertheless, it is important to understand the pluses and minuses of UGMAs before registering the shares in that form.