Manufacturing method for making a stator hollow structure for a shrouded propulsion rotary assembly for an aircraft; the stator hollow structure comprising at least: a central hub casing for a stator gearbox of the stator hollow structure; an external hollow duct surrounding the central hub casing; and between the central hub casing and the external hollow duct, at least three profiled guide vanes (6; 19), each profiled guide vane (6; 19) forming a fixed blade supporting the central hub casing; each profiled guide vane having a radial shank location and a radial tip location; each radial shank location being fixedly attached to the central hub casing and each radial tip location being fixedly attached to the external hollow duct; characterized in that the manufacturing method comprises the steps of: - at a preparing step, preparing separately from components of composite material at least three composite angular segments, so that each composite angular segment comprises: a core arched section of the central hub casing, a peripheral rim section of the external hollow duct and, between the core arched section and the peripheral rim section, a pair of angularly opposed sliced portions respectively for one profiled guide vane; and - at a finalizing step, finalizing the stator hollow structure from the composite angular segments once prepared; the finalizing step forming a unitary piece encompassing the overall shape of the stator hollow structure though a securing stage of forming the stator hollow structure in a unitary one-piece encompassing the overall shape; the securing stage providing securing together the continuously integrated composite angular segments. a central hub casing for a stator gearbox of the stator hollow structure; an external hollow duct surrounding the central hub casing; and between the central hub casing and the external hollow duct, at least three profiled guide vanes (6; 19), each profiled guide vane (6; 19) forming a fixed blade supporting the central hub casing; each profiled guide vane having a radial shank location and a radial tip location; each radial shank location being fixedly attached to the central hub casing and each radial tip location being fixedly attached to the external hollow duct; characterized in that the manufacturing method comprises the steps of: - at a preparing step, preparing separately from components of composite material at least three composite angular segments, so that each composite angular segment comprises: a core arched section of the central hub casing, a peripheral rim section of the external hollow duct and, between the core arched section and the peripheral rim section, a pair of angularly opposed sliced portions respectively for one profiled guide vane; and - at a finalizing step, finalizing the stator hollow structure from the composite angular segments once prepared; the finalizing step forming a unitary piece encompassing the overall shape of the stator hollow structure though a securing stage of forming the stator hollow structure in a unitary one-piece encompassing the overall shape; the securing stage providing securing together the continuously integrated composite angular segments. - at a preparing step, preparing separately from components of composite material at least three composite angular segments, so that each composite angular segment comprises: a core arched section of the central hub casing, a peripheral rim section of the external hollow duct and, between the core arched section and the peripheral rim section, a pair of angularly opposed sliced portions respectively for one profiled guide vane; and - at a finalizing step, finalizing the stator hollow structure from the composite angular segments once prepared; the finalizing step forming a unitary piece encompassing the overall shape of the stator hollow structure though a securing stage of forming the stator hollow structure in a unitary one-piece encompassing the overall shape; the securing stage providing securing together the continuously integrated composite angular segments.