Digital printing process on articles, each having a reference mark located around a respective extension axis, comprising: loading a plurality of articles on piece-holder assemblies distributed around a central axis of a rotatable drum, and each comprising at least a first spindle and a second spindle operable simultaneously in rotation by a same drive motor, each around a respective longitudinal axis; rotating the rotatable drum about said central axis to sequentially transfer said piece-holder assembly to a printing station; printing a printing pattern on a side surface of each article carried in the printing station, while the article is driven in rotation by the respective spindle (5a,5b); characterized in that, before transferring to the printing station, at least one of the articles is oriented around the respective spindle (5a,5b), to place the reference marks of the articles according to a same angular orientation around the respective extension axes, wherein the orientation of said at least one article around the respective spindle (5a,5b) comprises: simultaneously driving in rotation the spindles (5a,5b) being part of said piece-holder assembly; selectively stopping rotation of at least one of the articles during the rotation of the spindles (5a,5b), wherein during the simultaneous driving in rotation of the spindles (5a,5b) the following actions are performed: detecting the passage of the reference mark carried by the article loaded on a first spindle, at a first reading position localized around the extension axis of the first spindle; detecting the passage of the reference mark carried by the article loaded on a second spindle, at a second reading position located around the extension axis of the second spindle. loading a plurality of articles on piece-holder assemblies distributed around a central axis of a rotatable drum, and each comprising at least a first spindle and a second spindle operable simultaneously in rotation by a same drive motor, each around a respective longitudinal axis; rotating the rotatable drum about said central axis to sequentially transfer said piece-holder assembly to a printing station; printing a printing pattern on a side surface of each article carried in the printing station, while the article is driven in rotation by the respective spindle (5a,5b); characterized in that, before transferring to the printing station, at least one of the articles is oriented around the respective spindle (5a,5b), to place the reference marks of the articles according to a same angular orientation around the respective extension axes, wherein the orientation of said at least one article around the respective spindle (5a,5b) comprises: simultaneously driving in rotation the spindles (5a,5b) being part of said piece-holder assembly; selectively stopping rotation of at least one of the articles during the rotation of the spindles (5a,5b), simultaneously driving in rotation the spindles (5a,5b) being part of said piece-holder assembly; selectively stopping rotation of at least one of the articles during the rotation of the spindles (5a,5b), wherein during the simultaneous driving in rotation of the spindles (5a,5b) the following actions are performed: detecting the passage of the reference mark carried by the article loaded on a first spindle, at a first reading position localized around the extension axis of the first spindle; detecting the passage of the reference mark carried by the article loaded on a second spindle, at a second reading position located around the extension axis of the second spindle. detecting the passage of the reference mark carried by the article loaded on a first spindle, at a first reading position localized around the extension axis of the first spindle; detecting the passage of the reference mark carried by the article loaded on a second spindle, at a second reading position located around the extension axis of the second spindle.