If two players have the same total token value on a part I assume since neither player has control neither player can use the part. That means the tokens stay there for the next round. Does that sound right?
Good question! We will be clarifying this in the final rulebook and explicitly stating that when there is a tie no-one controls it. This gets a little fickle in the four player version as we have some slight rules adjustments for 4p and it will be extensively covered as well in the final rulebook!