  For a given Lovelock order $N$, it turns out that static fluid solutions of
the pure Lovelock equation for a star interior have the universal behavior in
all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and
the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of
$3$-space geometry. We employ the Buchdahl metric ansatz which encompasses
almost all the known physically acceptable models including in particular the
Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant
density star, always described by the Schwarzschild interior solution, defines
the most compact state of distribution while the other end is marked by the
Finch-Skea model, and all the other physically tenable models lie in between
these two limiting distributions.
