It is found herein that topology of amphiphiles immobilized on a porous solid of poly(high internal phase emulsion) (HIPE and polyHIPE) is critical to extraction pollutants from water. N-alkylation of branched polyethylenimine (bPEI) with a glycidylcapped polymer of poly(styrene-co-2-ethylhexyl acrylate) [P(S-EHA)] results in a dendritic amphiphile of bPEI@P(S-EHA), and a comb-like counterpart (lPEI@P(S-EHA) is similarly prepared by replacing bPEI with a linear PEI (IPEI). Each amphiphile can act as a stabilizer to directly prepare polyHIPE whose surface is dictated by the respective amphiphile. It is found that bPEI@P(S-EHA)-dictated polyHIPE can be over 50-fold stronger to eliminate anionic dyes from water than the linear counterpart, indicating a significant topological effect. The optimized adsorbent is over 10,000-fold stronger to bind a dye than a representative adsorbent, thus may deal with trace pollutants in water. (C) 2016 Wiley Periodicals, Inc.