An embodiment of the invention provides a prosthesis for placement at an Os opening from a main body lumen to a branch body lumen. The prosthesis comprises a radially expansible support and at least one frond extending axially from an end of the support. The support is configured to be deployed in at least a portion of a first body lumen, which can be a branch body lumen. At least one frond is extendable into across an ostium, e.g., from the first body lumen into a second body lumen, which may be a main body lumen.
