How Brazilian football system works - follow the thread:

Each one of the 27 Brazilian federative units (26 states+1 federal district) has its own league. Most of them are held from January to April. Out of these 27, 4 state leagues are considered to be the ones of highest level:
Campeonato Paulista(aka Paulistão - São Paulo state league),
Campeonato Carioca(Rio de Janeiro state league),
Campeonato Mineiro(Minas Gerais state league),
Campeonato Gaúcho(aka Gauchão - Rio Grande do Sul state league).

These tournaments have a vastly rich history in Brazil
and even though they've been losing popularity and importance over time, unlike many foreigners might think, they are NOT seen as simple preseason matches. It's not uncommon for example to see managers in big clubs get sacked due to bad results in these State Leagues.
Historically I'd say the importance given by big BR clubs and their supporters to these state leagues is comparable to the importance a Real fan gives to winning La Liga or a Bayern fan gives to winning Bundesliga. It might sound crazy, but it's not. I will explain better later,
but for now let's take a closer look at those four most important state leagues I mentioned a few tweets earlier:
Campeonato Paulista / São Paulo state league:

Held from January to April. Traditionally dominated by these four clubs:

Corinthians,
Santos,
São Paulo,
Palmeiras.

(listed in alphabetical order to avoid discussions of which is bigger)

All of these four are clubs that also
have both national and international relevance.

Other clubs from São Paulo state that also have had certain relevance over time are: Portuguesa, Guarani, Ponte Preta, Santo André, São Caetano, Bragantino(Red Bull Bragantino since 2019), Paulista, Ituano and a few others.
Campeonato Carioca / Rio de Janeiro state League:

Held from January to April. Traditionally dominated by these four clubs:

Botafogo,
Flamengo,
Fluminense,
Vasco da Gama.

(listed in alphabetical order again)

All of these four are clubs that also
have both national and international relevance.

Other clubs from Rio de Janeiro state that also have had certain relevance over time are: América, Bangu, and a few others.
Campeonato Mineiro / Minas Gerais state League:

Held from January to April. Traditionally dominated by these two clubs:

Atlético Mineiro,
Cruzeiro

(listed in alphabetical order again)

All of these two are clubs that also
have both national and international relevance.

Another club that can be listed as a very relevant 3rd force in this state: América Mineiro.
Campeonato Gaúcho / Rio Grande do Sul state League:

Held from January to April. Traditionally dominated by these two clubs:

Grêmio,
Internacional

(listed in alphabetical order again)

All of these two are clubs that also
have both national and international relevance.

Other clubs from Rio Grande do Sul state that also have had certain relevance over time are: Caxias, Juventude, Guarany, Novo Hamburgo, Brasil de Pelotas and a few others.
Besides these four state leagues, there are also a few others that, even though not as relevant as the four big ones, also have a somewhat high level of relevance. I will list the name of the state and their imporant clubs:
Paraná(Atlético Paranaense, Coritiba, Paraná Clube),

Santa Catarina(Figueirense, Avaí, Criciúma, Chapecoense),

Bahia(Vitória, Bahia),

Pernambuco(Sport, Náutico, Santa Cruz),

Ceará(Fortaleza, Ceará),

Goiás(Goiás, Atlético Goianiense, Vila Nova),

Pará(Paysandu, Remo).
As I mentioned, most of these are held from January to April (some less relevant state leagues are held for longer periods, but that information is not important to us).

Right after that, in April when the most relevant state leagues end, then finally
Campeonato Brasileiro (aka Brasileirão - in English: Brazilian league) starts. No big explanation needed, as its format is very similar to European leagues. The club with the highest amount of points gets the title, the best clubs get a spot in Libertadores or Sudamericana cup,
the worst clubs are relegated to 2nd tier. The main difference is that it runs from April to December.

Now, this begs the question:
One might say "every country has those two or three clubs that dominate the national league, who are they in Brazil?"

And the answer is:
NO! There are no 2-3 dominant clubs in Brazil. Remember the state leagues, that each of the most relevant state leagues has its own dominating clubs? When all those dominating clubs from different states play together in the Brazilian league, historically all of them have
managed to build their dominance in national level too. That means in total there are MORE THAN 12 dominant clubs when it comes to the Brazilian league: The 4 big clubs from the São Paulo state league, the 4 from Rio de Janeiro, the 2 from Minas Gerais and the 2 from
Rio Grande do Sul. Plus, in the last few decades clubs from Paraná, Bahia and Pernambuco states also have had very positive results, even managing to win both national and international tournaments.
Obviously there are discussions among fans of which club has a bigger history or most important titles, but there's no concrete answer for that. Depending on the perspective you can reach so many different conclusions on this.
In fact, the BR league is so hotly constested that the club with the biggest amount of titles ALL OVER THE HISTORY of the tournament actually has won it 10 times only. Completely different from French, Spanish or German leagues for example in which 1 or 2 clubs have won
the league over 10 times in less than 20 years.

One interesting consequence of this is that the Brazilian league is given a lot more importance by a Brazilian club or fan than a national league in Europe is given importance by an European club or fan.
Obviously another consequence is that the league is extremely unpredictable. Every year in April, right before the start of the league, there are always at least 6-10 clubs listed by the experts as favorites to win the title. Also it's not uncommon to see one of these listed as
favorites actually end up relegated to 2nd tier. In fact all big Brazilian clubs, literally all with no exceptions, have battled relegation at some point in the last few years, the majority of them ended up being relegated at least once.
As mentioned, the fact the league is contested by so many clubs makes winning it a very rare and hard accomplishment. League titles are seen by clubs and fans as huge titles with a major impact over the club's history. Fans also celebrate it as an once in life accomplishment.
I'm mentioning this because it's something those used to watch European leagues have a hard time understanding.

Summing up: Winning the STATE league is celebrated by club and fans the same way a big European club celebrates winning the NATIONAL league. And winning the BRAZILIAN
league is celebrated by fans not the same way an European celebrates the UCL title, but also not far from that, it's celebrated in a HIGHER INTENSITY than an European celebrates the national league title.
Now, besides the Brasileirão/Brazilian League, there's also another national competition: Copa do Brasil (in English: Brazil Cup/Brazilian Cup). Copa do Brasil format is also very similar to its equivalent in European leagues, so there's not much to say about it.
It runs from February to December and it can feature not only clubs from all 4 Brazilian league tiers, but also clubs that are not in any national tier (meaning they play their state league but haven't managed to qualify for any Brazilian league tier).
It's interesting to observe that this competion has grown a lot in relevance in the last decade, especially after 2013 when some changes were made.

The winner of this competition gets, besides the title obviously, a spot in the main continental competition: Libertadores.
And finally we have the Copa Libertadores da América, usually known as "Libertadores" only. It's the main continental competition, the South American equivalent to the Champions League. The top teams in Brazilian league table + winner of Brazilian cup get a spot to it.
Interesting commentary about Libertadores is that, after the first four editions in the 60's, due to many reasons, most Brazilian clubs started sending mostly backup players to Libertadores matches. Both the state leagues and Brazilian league were prioritized over Libertadores.
As mentioned, the careless attitude from Brazilian clubs towards Libertadores began to happen in the 1960's and only started to change in the 80's. Only in the 90's all Brazilian clubs really began to put their maximum effort into it.
As of today, Libertadores is now considered the most important competition by clubs and fans. Brazilian clubs playing in it are usually listed by experts among the favorites along with top Argentinian teams and a few others from different South American nations.
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