To provide a modified low molecular weight ethylenic polymer excellent in adhesiveness, printability, compatibility in polymer blends, mold releasability at high temperatures, fixability at low temperatures, dispersibility of pigments, initial lubricity, burnishing properties and the like, and application of the same.

The modified low molecular weight ethylenic polymer (B) having a hetero atom-containing group is prepared by treating a low molecular weight ethylenic polymer (A) defined by the following (i)-(vi). The low molecular weight ethylenic polymer (A) defined by the above (i)-(vi) is (i) a copolymer prepared by copolymerizing ethylene with at least one or more dienes or a copolymer prepared by copolymerizing ethylene with at least one or more olefins selected from 3-12C α-olefins and has (ii) 0.5-4.0 content of unsaturated group per one molecule, (iii) 870-980kg/m3 density, (iv) 70-130°C melting point, (v) 400-5,000 number average molecular weight and (vi) ≥4.0 Mw(weight average molecular weight)/Mn (number average molecular weight).