  Let X be a singular real rational surface obtained from a smooth real
rational surface by performing weighted blow-ups. Denote by Aut(X) the group of
algebraic automorphisms of X into itself. Let n be a natural integer and let
e=[e_1,...,e_l] be a partition of n. Denote by X^e the set of l-tuples
(P_1,...,P_l) of distinct nonsingular curvilinear infinitely near points of X
of orders (e_1,...,e_l). We show that the group Aut(X) acts transitively on
X^e. This statement generalizes earlier work where the case of the trivial
partition e=[1,...,1] was treated under the supplementary condition that X is
nonsingular. As an application we classify singular real rational surfaces
obtained from nonsingular surfaces by performing weighted blow-ups.
