  This paper is a sequel to the paper by A. Losev and Yu. Manin [LoMa1], in
which new moduli stacks $\bar{L}_{g,S}$ of pointed curves were introduced. They
classify curves endowed with a family of smooth points divided into two groups,
such that the points of the second group are allowed to coincide. The homology
of these stacks form components of the extended modular operad whose
combinatorial models are further studied in [LoMa2]. In this paper the basic
geometric properties of $\bar{L}_{g,S}$ are established using the notion of
weighted stable pointed curves introduced recently by B. Hassett. The main
result is a generalization of Keel's and Kontsevich -- Manin's theorems on the
structure of $H^*(\bar{M}_{0,S}).$
