1. AN OIL-SOLUTION HIGH MOLECULAR WEIGHT POLYMER CONTAINING A PLURALITY OF C8-C20 ALKYL GROUPS AND -S-(CH2)NX GROUPS ATTACHED TO DIFFERENT CARBON ATOMS OF A LINEAR HYDROCARBON CHAIN WHEREIN N IS INTEGER OF 1 TO 4 AND X IS A POLAR GROUP SELECTED FROM THE GROUP CONSISTING OF -COOR, -OR AND -NR2, AND R IS SELECTED FROM THE GROUP CONSISTING OF HYDROGEN AND C1-C10 ALKYL RADICALS SAID POLYER HAVING A SULFUR CONTENT OF FROM 1% TO 30% AND A MOLECULAR WEIGHT OF FROM 2000 TO 800,000 OBTAINED BY REACTING AN OMEGA-POLARSUBSTITUTED MERCAPTAN IN THE PRESENCE OF A CATALYST WITH A COPOLYMER OF A C4-C8 DIOLEFIN AND A POLYMERIZABLE OILSOLUBLE MONOMER CONTAINING A C8-C20 ALKYL RADICAL SELECTED FROM THE GROUP CONSISTING OF A-INSATURATED MONOOLEFIN HYDROCARBONS, OF C8-20 ALKYL ACRYLATES, VINYL ESTERS OF C8-20 FATTY ACIDS, VINYL ETHERS OF C8-20 ALKANOLS AND C8-20 ALKYL ACRYLAMIDES.