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Many process migration algorithms aim for transparency where neither the behaviour of the migrated process nor its appearance to the rest of the system is affected by the migration. However, there can be overheads associated with achieving transparency; maintaining communications after a migration can result in additional network traffic, increased system complexity, or both. This paper describes a taxonomy based upon the three basic techniques employed to support communications after a migration within a single network domain, compares the approaches taken in light of the number of peers, the life-span of the migrated process, the number of messages sent after a process migrates, communication delays, and whether the process undergoes a subsequent migration. Examples of existing migration algorithms are used to illustrate the taxonomy.