I believe it depends on the position of the player, offense of the team, certain situations in the game, game and shot clock, player's experience, HA/PA of the player(s), opposing OD, etc.
For example, if that high HA/PA player is a guard, and especially when the offense is one, like LI, where only the guards are required to have good HA/PA, then the GE does tend to put the ball in their hands more. In an offense like Low Post or PTB, if all 5 players have decent HA/PA for their positions, assists and distribution of the ball become balanced. At least that's what I have noticed.