2
\begin{figure}[H]
\centering
\begin{tikzpicture}[scale=0.7]
\Tree  [.Appl [.DP ] [.V [.DP ] [.v ] ]]
\end{tikzpicture}
\end{figure}

is giving me the above picture: enter image description here

But, what I really want is left skewed DP node without the v node. enter image description hereI want to eliminate the pixelated part.

2

You can draw explicit edges using the \edge command:

\documentclass{article}
\usepackage{tikz-qtree}
\begin{document}

\Tree  [.Appl [.DP ] [.V  DP \edge[draw=none]; {\phantom{XP}} ]]

\end{document}

I've used a \phantom{XP} node here instead of just {} so that the left branch angle is nicer.

output of code

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