Supported chromium catalysts with an average valence less than +6 and having a hydrocarbon-containing or halogenated hydrocarbon-containing ligand attached to at least one bonding site on the chromium are disclosed, as well as ethylene-based polymers with terminal alkane, aromatic, or halogenated hydrocarbon chain ends. Another ethylene polymer characterized by at least 2 wt. % of the polymer having a molecular weight greater than 1,000,000 g/mol and at least 1.5 wt. % of the polymer having a molecular weight less than 1000 g/mol is provided, as well as an ethylene homopolymer with at least 3.5 methyl short chain branches and less than 0.6 butyl short chain branches per 1000 total carbon atoms.