Before revision:  There has been considerable work on establishing upper bounds on the minimum cardinality such that any point set of that size admits an L-shaped embedding of any n-vertex tree with maximum degree 4.
After revision:  There has been considerable work on establishing upper bounds on the minimum cardinality such that any point set of that size admits an L-shaped embedding of any n-vertex tree with maximum degree 4 admits an L-shaped embedding on the point set.