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We introduce a class of spaces, called real cubings, and study the stuctureof groups acting nicely on these spaces. Just as cubings are a naturalgeneralisation of simplicial trees, real cubings can be regarded as a naturalgeneralisation of real trees. Our main result states that a finitely generatedgroup $G$ acts nicely (essentially freely and co-specially) on a real cubing ifand only if it is a subgroup of a graph tower (a higher dimensionalgeneralisation of $\omega$-residually free towers and NTQ-groups). It followsthat $G$ acts freely, essentially freely and co-specially on a real cubing ifand only if $G$ is a subgroup of the graph product of cyclic and(non-exceptional) surface groups. In the particular case when the real cubingis a tree, it follows that $G$ acts freely, essentially freely and co-speciallyon the real cubing if and only if it is a subgroup of the free product ofabelian and surface groups. Hence, our main result can be regarded as ageneralisation of the Rips' theorem on free actions on real trees.  We apply our results to obtain a characterisation of limit groups overpartially commutative groups as subgroups of graph towers. This resultgeneralises the work of Kharlampovich-Miasnikov, \cite{KhMNull}, Sela,\cite{Sela1} and Champetier-Guirardel, \cite{CG} on limit groups over freegroups.

Group Actions on Real Cubings and Limit Groups over Partially Commutative Groups