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A child association can be thought of as an aggregate in UML terms. That is, the parent effectively owns the children, and as such, operations like delete etc will propagate through the children. Each child is given a name within the parent and it's possible to specify whether the names of children should be unique or not within the parent. Child associations are easily navigable using Alfresco's XPath and Lucene search languages.
Unlike child associations, delete propagation does not take place and there is no notion of naming the associated node. Alfresco's search languages do not yet support joins across non-child associations.