We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted labelled trees of important combinatorial tree families including labelled ordered, unordered and binary trees. Using combinatorial decompositions of the underlying structures yields, after solving the resulting equations, implicit characterizations of suitable generating functions of the total number of such tree parking functions for trees of size n and n successful drivers, from which we obtain exact and asymptotic enumeration results. The approach can be extended to the general situation of tree parking functions for trees of size n and $m<n$ drivers for which we are also able to characterize the generating functions solutions, which allow, by applying analytic combinatorics techniques, a study of the asymptotic behaviour of the total number of tree parking functions and distributions for $n\to \infty$ depending on the load factor $0<\alpha =\frac{m}{n}<1$.

我们研究了最近引入的各种树停车功能的枚举问题，称为树停车功能，树停车分布，主要树停车功能和主要树停车分布，用于重要组合树族的有根标签树，包括带标签的有序，无序和有序的树。二叉树。使用基础结构的组合分解，在求解所得方程式之后，隐式表征了大小为n和n的成功驾驶员树的此类泊车函数总数的合适生成函数，从中我们获得了精确的渐近枚举结果。该方法可以扩展到大小为n的树的树停车功能的一般情况 和 $米<ñ$ 我们还能够表征生成函数解决方案的驱动程序，通过应用分析组合技术，可以研究树停车函数总数和其分布的渐近行为 $ñ\to \infty$ 取决于负载系数 $0<\alpha =\frac{米}{ñ}<\mathrm{1个}$。