Our　first　aim　of　this　paper　is　to　define　maximal　operators　of　a-quadratic　variation　and　of　a-conditional　quadratic　variation　for　vector-valued　tree　martingales　and　to　show　that　these　maximal　operators　and　maximal　operators　of　vector-valued　tree　martingale　transforms　are　all　sublinear　operators.　The　second　purpose　is　to　prove　that　maximal　operator　inequalities　of　a-quadratic　variation　and　of　a-conditional　quadratic　variation　for　vector-valued　tree　martingales　hold　provided　2　＜=　a　＜　infinity　by　means　of　Marcinkiewicz　interpolation　theorem.　Based　on　a　result　of　reference　[10]　and　using　Marcinkiewicz　interpolation　theorem,　we　also　propose　a　simple　proof　of　maximal　operator　inequalities　for　vector-valued　tree　martingale　transforms,　under　which　the　vector-valued　space　is　a　UMD　space.