We describe the synthesis and characterization of a number of polymers with well-defined structures that serve as models for polyethylene with long chain branching. All of them have been made by using anionic polymerization techniques and controlled chlorosilane chemistry to give nearly monodisperse polybutadienes with precise control of the number, length, and placement of long ((M) over bar(w) > 1500 g/mol) branches on each chain. This was followed by hydrogenation to give saturated polymers with the same well-defined long chain branching and the local structure of a typical linear low-density polyethylene. That is, both the backbones and the long branches had 17-25 ethyl branches per 1000 total carbons. Among the structures made were some with no long branches ("linears"), some with a single long branch ("stars"), others with exactly two branch points (the alpha-omega type, "H＇s", "super-H＇s", and "pom-poms"), and some with several long branches randomly distributed along the backbone ("combs"). Essentially all types of branching from a linear backbone can be made by the techniques described herein. While linear and symmetrical star models of polyethylene have been made previously, the other structures are the first examples of polyethylene models with multiple branches and precise control of the molecular architecture. We use the results given here to discuss how long chain branching can be detected in polyethylene. We also show how the branching structure controls chain dimensions. The Zimm-Stockmayer model works well to describe the sizes of the lightly branched molecules, but its predictions are too small for those with many long branches. This is presumably due to crowding of the branches. The rheological properties of these polymers will be described in subsequent publications.