Not that miraculously. More like the CIA financed and trained in France a terrorist attract to kill the person that Franco has selected as successor, Carrero Blanco and then appointing the most stupid person in the regime, Arias Navarro.
The "successful" transition to democracy was initiated by stupid decisions like giving the Sahara territories to Morroco so they can slaughter the native population and occupy it with Morrocan(It should have been given independence instead) and creating the State of Autonomias.
The State of Autonomias was the transition from a highly centralized State, to one of the more decentralized countries on Earth.
It was done this way in order to appease the Independentist that were a minority at the time,(In Catalunia a 6-12%) and now in places like Catalunia and Vasque country are becoming near to a majority(50%).
The electoral system in Spain(chosen in the "succesful" transition to democracy, favored minorities over majorities giving way more representation than they should have.
They made the effective eradication of the use of Spanish, even in places like Basque country(the Spanish language comes from the territory between it and Cantabria) in education and brainwashing of kids propagating hatred against anything spanish.
That was also helped by the terrorist organization ETA that just killed and ostracized those that were not secessionist in Basque country.
In Catalunia kids were taught that Catalonia were a kingdom in the past(never happened), the myth of the Segadors as independentist when they were a movement against the rich or that the war for Sucesion(succession) was a war for Secession in Catalunia.
BTW, this lie is the the linked article.
This is all false and very easy for anyone to check, because Truth doesn't matter because when repeating a lie a thousand times it becomes a truth. And they controlled local TV and education for 40 years.
They even meet each year in front of a guy called Rafael Casanovas as a secession leader when every time he talked always finished with a "Viva España"(long live Spain).
Spanish history is no more violent than that of the rest of European countries, or the UK and US(that have fought or invaded most of the countries on the rest of the world).