We study Choquard type equation of the form [graphic not available: see fulltext] where N≥3\documentclass[12pt]{minimal}
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\begin{document}$$N\ge 3$$\end{document}, Iα\documentclass[12pt]{minimal}
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\begin{document}$$I_\alpha $$\end{document} is the Riesz potential with α∈(0,N)\documentclass[12pt]{minimal}
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\begin{document}$$\alpha \in (0,N)$$\end{document}, p>1\documentclass[12pt]{minimal}
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\begin{document}$$p>1$$\end{document}, q>2\documentclass[12pt]{minimal}
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\begin{document}$$q>2$$\end{document} and ε≥0\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon \ge 0$$\end{document}. Equations of this type describe collective behaviour of self-interacting many-body systems. The nonlocal nonlinear term represents long-range attraction while the local nonlinear term represents short-range repulsion. In the first part of the paper for a nearly optimal range of parameters we prove the existence and study regularity and qualitative properties of positive groundstates of (P0)\documentclass[12pt]{minimal}
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\begin{document}$$(P_0)$$\end{document} and of (Pε)\documentclass[12pt]{minimal}
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\begin{document}$$(P_\varepsilon )$$\end{document} with ε>0\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon >0$$\end{document}. We also study the existence of a compactly supported groundstate for an integral Thomas–Fermi type equation associated to (Pε)\documentclass[12pt]{minimal}
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\begin{document}$$(P_{\varepsilon })$$\end{document}. In the second part of the paper, for ε→0\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon \rightarrow 0$$\end{document} we identify six different asymptotic regimes and provide a characterisation of the limit profiles of the groundstates of (Pε)\documentclass[12pt]{minimal}
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\begin{document}$$(P_\varepsilon )$$\end{document} in each of the regimes. We also outline three different asymptotic regimes in the case ε→∞\documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon \rightarrow \infty $$\end{document}. In one of the asymptotic regimes positive groundstates of (Pε)\documentclass[12pt]{minimal}
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\begin{document}$$(P_\varepsilon )$$\end{document} converge to a compactly supported Thomas–Fermi limit profile. This is a new and purely nonlocal phenomenon that can not be observed in the local prototype case of (Pε)\documentclass[12pt]{minimal}
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\begin{document}$$(P_\varepsilon )$$\end{document} with α=0\documentclass[12pt]{minimal}
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\begin{document}$$\alpha =0$$\end{document}. In particular, this provides a justification for the Thomas–Fermi approximation in astrophysical models of self-gravitating Bose–Einstein condensate.
