We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2,2m - 1) minimal model coupled to two-dimensional Euclidean quantum gravity. Furthermore, we show that the principal (r,s) ZZ brane can be viewed as the basic (1,1) ZZ boundary state tensored with a (r,s) Cardy boundary state for a general (p,q) minimal model coupled to two-dimensional quantum gravity. In this sense there exists only one ZZ boundary state, the basic (1,1) boundary state.

PACS numbers: 11.25.Pm, 11.25.Hf, 04.60.Nc, 04.60.--m