A power transmission device for an aircraft turbomachine, comprising: - a mechanical reducer comprising a central gear and an outer ring gear coaxial with one another around a main axis of rotation, and planet gears meshing with the central gear and the outer ring gear, the outer ring gear comprising two half-ring gears (50A, 50B) each having an outer annular flange (52A, 52B) attached to one another, - a plurality of first oil ejection channels contained in a first radial plane perpendicular to the main axis of rotation, formed between the annular flanges (52A, 52B) and configured to eject lubrication oil by centrifugal force, - a gutter for recovering lubrication oil, annular around a central axis, and comprising, in a section plane parallel to the central axis, a first radial wall extending radially with respect to the central axis, at least a first wall inclined with respect to the first radial wall and extending from one outer radial end of the first radial wall, a guide portion having an overall U-shape extending from one end of the inclined wall, and a second radial wall extending radially outward with respect to the central axis from one end of the guide portion, a space delimited by the first radial wall, the second radial wall and the at least first inclined wall forming a lubrication oil intake chamber, and a space delimited by the guide portion and the second radial wall forming a lubrication oil evacuation cavity, the gutter being radially disposed around the annular flanges (52A, 52B), such that the intake chamber of the gutter is radially facing the first oil ejection channels, the device comprising a rotor shaft having a rotor flange attached to one of the annular flanges (52A, 52B) of the outer ring gear, and at least a second radial plane perpendicular to the main axis of rotation and comprising a plurality of second oil ejection channels formed between the rotor flange and said one of the annular flanges (52A, 52B), the at least one second radial plane being axially offset with respect to the first radial plane, characterized in that the gutter comprises a second inclined wall delimitating, with the first radial wall, the second radial wall and the first inclined wall, the space forming the lubrication oil intake chamber, and in that the first and the second inclined wall (121, 122) are each disposed on the first and on the second radial plane (P1, P2) respectively, the first inclined wall forming a first angle (α) with the first radial plane, and the second inclined wall forming a second angle (α') with the second radial plane, the first angle (α) being smaller than the second angle (α') when the first radial plane is further from the second radial wall than the second radial plane, and conversely. - a mechanical reducer comprising a central gear and an outer ring gear coaxial with one another around a main axis of rotation, and planet gears meshing with the central gear and the outer ring gear, the outer ring gear comprising two half-ring gears (50A, 50B) each having an outer annular flange (52A, 52B) attached to one another, - a plurality of first oil ejection channels contained in a first radial plane perpendicular to the main axis of rotation, formed between the annular flanges (52A, 52B) and configured to eject lubrication oil by centrifugal force, - a gutter for recovering lubrication oil, annular around a central axis, and comprising, in a section plane parallel to the central axis, a first radial wall extending radially with respect to the central axis, at least a first wall inclined with respect to the first radial wall and extending from one outer radial end of the first radial wall, a guide portion having an overall U-shape extending from one end of the inclined wall, and a second radial wall extending radially outward with respect to the central axis from one end of the guide portion, a space delimited by the first radial wall, the second radial wall and the at least first inclined wall forming a lubrication oil intake chamber, and a space delimited by the guide portion and the second radial wall forming a lubrication oil evacuation cavity, the gutter being radially disposed around the annular flanges (52A, 52B), such that the intake chamber of the gutter is radially facing the first oil ejection channels, the device comprising a rotor shaft having a rotor flange attached to one of the annular flanges (52A, 52B) of the outer ring gear, and at least a second radial plane perpendicular to the main axis of rotation and comprising a plurality of second oil ejection channels formed between the rotor flange and said one of the annular flanges (52A, 52B), the at least one second radial plane being axially offset with respect to the first radial plane, characterized in that the gutter comprises a second inclined wall delimitating, with the first radial wall, the second radial wall and the first inclined wall, the space forming the lubrication oil intake chamber, and in that the first and the second inclined wall (121, 122) are each disposed on the first and on the second radial plane (P1, P2) respectively, the first inclined wall forming a first angle (α) with the first radial plane, and the second inclined wall forming a second angle (α') with the second radial plane, the first angle (α) being smaller than the second angle (α') when the first radial plane is further from the second radial wall than the second radial plane, and conversely.