Portuguese, as well as Spanish, doesn't distinguish between a situation where one object floats over another, "The lamp hangs over the table", without directly touching it and a situation where one object is on another object, "The pencil is on the table", with direct contact.
O copo está sobre a mesa.
The glass is on the table.
A lâmpada paira sobre a mesa.
The lamp hangs over the table.
For on / upon Portuguese has a second preposition, em cima. One could believe that this preposition is used when there is no contact, but this is not the case. Sobre and em cima are synonyms. En both cases there can be a contact or not. Sometimes one can find that por cima is used if there is no contact, what is indeed true, but doesn't change anything. Por cima is used to describe a mouvement, "The airplane flies over the city". Por cima is used when an object passes over another object. In this case there is obviously no contact. If an airplane flies over a city an have a contact with this city we have two problems. The passengers won't feel confortable and the airplane will stop flying over the city. Por cima describes a mouvement. If a helicopter circles over a city, it is sobre or cima. This is a mouvement as well, but not from point A to point B.
em cima on, em cima = above, por cima = over
Os livros foram deixados em cima da mesa.
The books have been laid on the table.
Um helicóptero voa em cima da cidade.
A helicopter circles above the city.
O avião voou por cima da montanha.
The airplane flies over the mountains.
The prepositions em / por + cima are not joined. The preposition a + cima are joined to acima. Sobre cannot be used with any other preposition.
cima with por, em, a
O que você está pedindo está acima das minhas capacidades.
What you desire is beyond my possibilities.
Ainda por cima, nem sequer inscreveram essa questão na agenda.
On top they did not even put this point on the agenda.
Pensamos que o melhor é colocar uma pedra em cima do assunto.*
We believe that the best thing to do is to put an end to this issue.
Voam à volta, mas não passam por cima.
They flew around, but not above.
* literally: ...to put a stone one something
For unknown reasons the human brain tends to transpose relationships in space to hierarchical relationships. That is so natural that most people do not even see that this is strange. However it is strange. If a distinction is made, sometimes, between relationships in space and relationships in time, Before twelve o' clock <=> In front of the door, it would be more logical as well to distinguish between a hierarchical and a spatial relationship. (In german many spatial relationships are transposed to relationships in time: Vor zwölf Uhr (Bevor twelve o' clock) <=> Vor der Tür (In front of the door)).
The book lies under the table.
Under his reign science and art florished.
Some people may say that this is pure coincidence. However if we use the same prepositions to describe two very different relationships in any language, it can't be pure coincidence.
Acima and em cima can describe relationships in time and can be used as well metaphorically.
Ninguém esta acima da lei.
Ninguém esta em cima da lei.
Nobody is above the law.
In the description of relationships in space sobre and em cima are interchangeable.
interchangeability em cima / sobre
O livro esta sobre a mesa.
O livro esta em cima da mesa.
The book is on the table.
However in general sobre and em cima are not interchangeable. Verbs that can connect an issue (to talk about, to discuss about, to speculate about) as well as nouns that connect to an issue (an article about, the controll over, a study about) connects with sobre. The preposition em cima cannot be used in this context. ~Falam acima dele is wrong. It is Falam sobre ele.
verbs with sobre
Dizem que ele vaga pelos arredores do mundo, reaparecendo quando falam sobre ele.
It is said that he wanders on earth and only shows up, if one speaks about him.
Mas vocês conversaram sobre isso, certo?
But you have talked about it, right?
Eu sei que você mentiu sobre a mulher.
I know that you have lied about this woman.
nouns with sobre
É uma pesquisa sobre o consumo de cerveja.
It is a study about the consumption of beer.
O texto abaixo é parte de um artigo sobre a História dos Números.
The text below is an article about the history of numbers.
Only in a context of relationships in space sobre competes with em cima de / acima de.
(acima de shouldn't be confused with acima. Acima is an adverb, see 21.2.5.)
In all other cases of metaphorical use it is acima de.
only acima possible
Ela está acima de qualquer suspeita.
She is beyond all suspicion.
Juros acima de 4% fazem soar alarmes.
Interest rates beyond 4 percent set alarm clocks ringing.
Acredita num crescimento acima de 2,5%.
He believes in a growth of 2,5 percent.
Acima alone is an adverb and corresponds to the English above. (Altough above is preposition and adverb. => adverb: ...as stated above, => preposition: above all suspicion.)
acima as an adverb
Leia o texto acima.
Read the text above.
Hoje eu estacionei o carro mais acima.
Today I parked the car further above.
Only cima can be combined with other prepositions. This is necessary if we want to describe more complex relationships.
Para cima means on in the sense that there is a mouvement to a place and por cima describes a mouvement as well, but without contact.