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I want to extrude a curve into two directions.

curve

Otherwise, join both curves into one, it is possible? I've tried copying it and then join segments, but it don't see a Remove Doubles tool while working on curves.

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  • $\begingroup$ There is the Split option in the Curve menu that's available in Edit mode. I believe it just joins another curve to the current one, though. $\endgroup$ – Anthony Forwood Jul 6 '16 at 4:25
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Not supported in Blender, curve vertex must always belong to a maximum of two segments.

Either use a mesh object with a Skin modifier instead, if you require true 'branching' and a continuous mesh surface.

Skin modifier

Or if you prefer curve objects duplicate a vertex in place, leave it overlapping the original one, and then extrude the new one; if you don't mind the discontinuity in the mesh.

Curve branching

You can just directly select any middle vertex and extrude it twice with E, the first extrude will duplicate the vertex automatically Right-Click to cancel and the second extrude will start a new branch.

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