  We present an analysis of the structure and properties of chromatic
polynomials $P(G_{pt,\vec m},q)$ of one-parameter and multi-parameter families
of planar triangulation graphs $G_{pt,\vec m}$, where ${\vec m} =
(m_1,...,m_p)$ is a vector of integer parameters. We use these to study the
ratio of $|P(G_{pt,\vec m},\tau+1)|$ to the Tutte upper bound $(\tau-1)^{n-5}$,
where $\tau=(1+\sqrt{5} \ )/2$ and $n$ is the number of vertices in $G_{pt,\vec
m}$. In particular, we calculate limiting values of this ratio as $n \to
\infty$ for various families of planar triangulations. We also use our
calculations to study zeros of these chromatic polynomials. We study a large
class of families $G_{pt,\vec m}$ with $p=1$ and $p=2$ and show that these have
a structure of the form $P(G_{pt,m},q) = c_{_{G_{pt}},1}\lambda_1^m +
c_{_{G_{pt}},2}\lambda_2^m + c_{_{G_{pt}},3}\lambda_3^m$ for $p=1$, where
$\lambda_1=q-2$, $\lambda_2=q-3$, and $\lambda_3=-1$, and $P(G_{pt,\vec m},q) =
\sum_{i_1=1}^3 \sum_{i_2=1}^3 c_{_{G_{pt}},i_1 i_2}
\lambda_{i_1}^{m_1}\lambda_{i_2}^{m_2}$ for $p=2$. We derive properties of the
coefficients $c_{_{G_{pt}},\vec i}$ and show that $P(G_{pt,\vec m},q)$ has a
real chromatic zero that approaches $(1/2)(3+\sqrt{5} \ )$ as one or more of
the $m_i \to \infty$. The generalization to $p \ge 3$ is given. Further, we
present a one-parameter family of planar triangulations with real zeros that
approach 3 from below as $m \to \infty$. Implications for the ground-state
entropy of the Potts antiferromagnet are discussed.
