As with many other verbs, you can add prefixes to portar to give it new meanings. Although the basic meaning of portar is "to carry" or, in some cases, "to bear," its meanings with prefixes have evolved over time and thus usually aren't obvious. Although most of them have English cognates, the meanings in the two languages sometimes differ.
Here are the most common meanings of portar and related verbs, along with sample sentences. Note that in some cases, the reflexive verb forms can have substantially different meanings:
aportar: to provide, to contribute, to arrive at a port. Los esclavos africanos aportaron mucho a la cultura de la isla caribeña. African slaves contributed to the culture of the Caribbean island.
deportar: to deport. Although not common, the reflexive deportarse can refer to resting or enjoying oneself. Japón estudia deportar a 14 activistas chinos acusados de entrada ilegal en el país. Japan is studying exporting 14 Chinese activists accused of illegal entry in the country.
comportar: to involve, to bring about, to entail. La anestesia general comporta más riesgos que la epidural. General anesthesia involves more risks than epidural anesthesia.
comportarse: to behave, to conduct oneself. Se comportaban como dos tontos. They were behaving like two fools.
exportar: to export. ¿Cuales son los productos que exportan el Ecuador a Estados Unidos? What products does Ecuador export to the United States?
importar: to matter, to be important, to import. No me importa que hablen mal de mí. It doesn't matter to me that they speak poorly of me. El país importa muchos de los alimentos que consume. The country imports much of the food it consumes.
portar: To carry or to bear, often in a broad sense meaning "to use" or "to have." Este mecanismo se emplea en los vehículos que portan una transmisión manual. This mechanism is used in vehicles that have a manual transmission.
portarse: to behave (note that in English, one can talk about a person's behavior by referring to the way a person carries him- or herself), similar to comportar. Pero en algún momento todos nos portamos mal. But at some time we all behave poorly.
reportar: to yield, to produce. Influence from English has also given the verb the meaning of "to report," especially in Latin America. Dejar el hábito de fumar reporta grandes beneficios para la salud. Quitting the smoking habit yields great health benefits. La cadena de televisión reportó que hasta ocho personas habían resultado heridas por el atacante. The television network reported that as many as eight people were injured by the attacker.
soportar: to withstand, to endure (either physically or emotionally). Alex no soportó más el dolor y se tiró al piso en un gesto de desespero. Alex couldn't stand the pain any more and he threw himself to the floor in an expression of hopelessness.
transportar, trasportar: to transport. Los ferrocarriles de Ucrania en cinco meses desde el principio del año transportaron 9,56 millones de toneladas de los cereales. In the five months since the beginning of the year, Ukrainian railroads transported 9.56 million tons of grain.
Related words: Other words related to portar include el comportamiento (behavior), el deporte (sport), la importancia (importance), el pasaporte (passport), la puerta (door), el puerto (port), el soporte (support) and la transportación (transportation).
References: Sample sentences are adapted from a variety of sources. Among those consulted for this lesson are Mecánica Online, Calle 13, es.Yahoo.com, elQuieto.com, Grupo Anarquista Bifucación, Madrid.org, Tumblr.com, es.Answers.com and Líderendeportes.