  Maximally symmetric curved-brane solutions are studied in dilatonic
braneworld models which realise the self-tuning of the effective
four-dimensional cosmological constant. It is found that no vacua in which the
brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the
near-boundary asymptotics of the bulk fields. In the holographic dual picture,
this corresponds to coupling the UV CFT to a curved metric (possibly with a
defect). Alternatively, the same may be achieved in a flat-space QFT with
suitable variable scalar sources. With these ingredients, it is found that
maximally symmetric, positive and negative curvature solutions with a
stabilised brane position generically exist. The space of such solutions is
studied in two different types of realisations of the self-tuning framework. In
some regimes we observe a large hierarchy between the curvature on the brane
and the boundary UV CFT curvature. This is a dynamical effect due to the
self-stabilisation mechanism. This setup provides an alternative route to
realising de Sitter space in string theory.
