Two Nominals
A nominal is a subtree headed by a common noun (NOUN), proper noun (PROPN) or pronoun (PRON). Some nominals may be headed by a symbol (SYM) if it represents a noun. Other words such as adjectives, numerals or determiners can be promoted to the head position if the main noun is elided. And words of most categories can act as nominals if they are mentioned rather than used. Note that the term ‘subtree’ is meant here to include selected but not necessarily all descendants of the head. A nominal may act as a predicate of a clause and then some of its dependents will attach at the clausal level and will not be considered part of the nominal.
There is a number of options how to connect two nominals with a relation. The first question to answer is whether one of the nominals is a clear head and the other clearly modifies it. In the typical case, the modifier nominal can be removed without rendering the sentence ungrammatical, and it refines the meaning of the head nominal. For example, English border patrol denotes a special type of patrol, and the man with the yellow hat is a special type of man. On the other hand, semantic compositionality is not a necessary condition and head-dependent relations are extended to similarly connected nominals where the meaning is noncompositional: for instance, a prairie dog is not a dog (neither a prairie).
If there is a clear head
The default relation between the head and the modifier nominal is nmod. Some languages may have language-specific criteria that allow to separate noun-noun compounds from other noun-noun modifications; then the compound relation is used. (Note that this relation can be also used for compounds where the parts are not nominals.) In other languages, such as German or Swedish, noun-noun compounds are written as one word and the compound relation is not needed. In yet other languages, the traditional grammar may define compounds on semantic grounds but their morphosyntactic behavior does not differ from ordinary head-modifier structures, so there is no reason not to use the nmod relation. For example, French chemin de fer (lit. path of iron) “railroad” follows the same syntactic pattern as other, more compositional noun-noun modifications.
English is an example of a language where it makes sense to use the compound relation to connect two nominals. In noun-noun compounds, the dependent nominal precedes the head nominal, and there are restrictions on how the dependent nominal itself can be further modified. A determiner can precede the whole compound (the prairie dog) but it cannot be inserted between the modifier and the head (*the prairie the dog); the determiner before the compound modifies directly the head of the compound, not its first part. The head can be pluralized but the modifier cannot. On the other hand, in the ordinary nmod relation the modifier usually has some sort of case marking, either the possessive suffix (the dog’s tail) or a preposition (the tail of the dog). In both cases the modifier can be pluralized and can have its own determiner (in the case of a prepositional modifier, both the head and the modifier can have a determiner). Remember that these rules are specific to English; other languages may have different rules or may not be able to separate compound from nmod at all.
If there is no clear head
Several relations are available and they are always directed from the first nominal to the second nominal (in the order of utterance, i.e., they go left-to-right if the language uses a left-to-right writing system).
If the two nominals denote two different entities that together have the same grammatical function in the sentence, they are connected with the conj relation and we have coordination of nominals. Coordination is typically recognizable by a coordinating conjunction (CCONJ) but it is not a requirement. There are examples of asyndetic coordination where the conjuncts are delimited by a comma or pause, as in English Sunlight lit up the fine hairs on her arm, the embroidered flowers on the collar of her white shirt.
If the two nominals participate in denoting one entity, the default relation to connect them is flat (which may also be used to connect other nodes that are not nominals). Typical examples are personal names: we can say that John Smith is a special type of John as well as a special type of Smith, but none of the names governs the other and either of them can be omitted. In many languages this analysis extends to titles and occupations, as in English president Barack Obama.
Some languages may have language-specific criteria that allow to separate apposition from simple flat sequences of nouns; then the appos relation is used. For example in English, the criterion is that the second (i.e., technically dependent) nominal in apposition can have its own determiner and possibly other modifiers; the two nominals are typically separated by a comma in writing: in Robert Mugabe, the former president of Zimbabwe, there is a flat relation from Robert to Mugabe, an appos relation from Robert to president, and an nmod relation from president to Zimbabwe. Furthermore, in appositions the two nominals can typically be reordered: the former president of Zimbabwe, Robert Mugabe. Note that non-UD grammars and theories may use a broader notion of apposition, which covers constructions that will not lead to the appos relation in UD. Also remember that the rules in this example are specific for English. Other languages may have different rules or may not be able to separate appos from flat at all.