The Spanish word 'trámite' (meaning 'procedure' or 'administrative step') comes from the Latin word 'tramitem' (accusative of 'trames'), which meant 'path' or 'way'. The Latin 'trames' itself was formed from two parts: the prefix 'trans-' meaning 'across' and the verb 'meare' meaning 'to pass' or 'to flow'. So etymologically, a 'trámite' is like a path that one crosses or flows through.

The meaning evolved from a physical path that one would traverse to a more abstract sense of a procedure or step that one must go through, particularly in administrative or bureaucratic contexts. This semantic shift from concrete to abstract meaning is quite common in language evolution.

While 'trámite' itself is a commonly used word in Spanish bureaucratic language, there are related words like 'tramitación' (processing) and 'tramitar' (to process, to carry out a procedure). These words share the same root and maintain the concept of following a established path or process.

While there aren't many common English words directly related to 'trámite', we can find the same Latin 'trans-' prefix in many English words like 'transport' (to carry across), 'transmit' (to send across), and 'traverse' (to cross over). Understanding this prefix can help remember that 'trámite' involves going through or across a process.