Bubbling convergence results for approximate harmonic maps, based on : Ding, Weiyue; Tian, Gang; Energy identity for a class of approximate harmonic maps from surfaces; Commun. Anal. Geom. 3, No. 4, 543-554 (1995). (See also: Wang, Changyou; Bubble phenomena of certain Palais-Smale sequences from surfaces to general targets; Houston J. Math. 22, No. 3, 559-590 (1996), and: Parker, Thomas H.; Bubble tree convergence for harmonic maps; J. Differ. Geom. 44, No. 3, 595-633 (1996).)