One Dundee nursery is waiving registration fees and offering care on an hourly basis.
An Aberdeen charity says it has been inundated with requests from parents.
The new legal right is known as Jack's Law, in memory of 23-month old Jack Herd who drowned in a pond in 2010.
Lady Smith’s call for evidence comes ahead of the Phase 6 case study, which begins this summer.
The Labour-led Scottish Executive felt an inquiry 'was not the best way to proceed'.
