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Hi guys. Do these sound o.k. to you? Thank you for your help.

It came out that the event of the last year turned out to be an appearance of a new social network.
The event of the year came out to be a birth of a new social network.
The most important event in the last year turned out to be a revealing of a new social network.
The revealing of a new social network last year became the most important event, Google said.
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I don't really like any of them. Try this modified version of the third.
The most important event in the last year turned out to be the unveiling of a new social network.
It came out that The event of (the) last year turned out to be the appearance of a new social network. -- "came out ... turned out" is awkward.

The event of the year came turned out to be the birth of a new social network.

The most important event in the last year turned out to be a revealing of the launch/emergence/etc. of a new social network. -- "a revealing of" is not right; several words will fit here, depending on the meaning you want.

The revealing of a new social network last year became the most important event, Google said. -- Seems generally awkward.
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Thank for the answers, guys. So "if the fact comes out" it means "it's avaliable right now and it becomes known". Is that right?
Mr WordyIt came out that The event of (the) last year turned out to be the appearance of a new social network. -- "came out ... turned out" is awkward.
Because there are two phrasals with quite the same meaning. Is that so?
Mr WordyThe revealing of a new social network last year became the most important event, Google said. -- Seems generally awkward.
Will "unveiling, the launch" make up for the awkwardness?
FandorinThank for the answers, guys. So "if the fact comes out" it means "it's avaliable right now and it becomes known". Is that right?

If a fact "comes out" then, yes, it becomes known, but often there's the connotation that it leaked out rather than being deliberately publicised.
Fandorin
Mr WordyIt came out that The event of (the) last year turned out to be the appearance of a new social network. -- "came out ... turned out" is awkward.
Because there are two phrasals with quite the same meaning. Is that so?
There are several contributing factors: (i) the similar meanings, as you say; (ii) the meaning of "came out" doesn't quite seem to quite fit the sentence; (iii) the simple repetition of "out".
Fandorin
Mr WordyThe revealing of a new social network last year became the most important event, Google said. -- Seems generally awkward.
Will "unveiling, the launch" make up for the awkwardness?
Replacing "revealing" with "unveiling" or "launch" fixes one problem. Another is "... last year became the most important event ...". This seems "unfinished" and seems to need some more qualification. In what sphere, or sense, was it "the most important event"?

"... was the most important event of last year", on the other hand, is OK because "of last year" seems to provide the required qualification. (Of course, further qualification is assumed to be applied by the context; the statement is not plausibly true in any universal sense.)
I see it now.
Mr WordyThis seems "unfinished" and seems to need some more qualification. In what sphere, or sense, was it "the most important event"?
It was just the spur of the moment I decided upon making up a sentence. It was some kind of nomination.

The unveiling of a new social network (of) last year (the event) became the most important event in .ru domain and won one of the Google's nomination prizes as "the most important and expected social resource".

Is it significant to leave or not to leave of in this case? Having been provided with some information, it became better, is that so?

Thank you so much, Mr. Wordy.
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Fandorin
The unveiling of a new social network (of) last year (the event) became the most important event in .ru domain and won one of the Google's nomination prizes as "the most important and expected social resource".

Is it significant to leave or not to leave of in this case? Having been provided with some information, it became better, is that so?


Yes, the addition of "in the .ru domain" helps to "round off" the thought, I think.

"The unveiling of a new social network (of) last year (the event) became the most important event in the .ru domain and won one of the Google's ..."

The last part of the sentence doesn't work. You can be "nominated" for a prize, and you can "win" a prize, but there is no such thing, as far as I know, as a "nomination prize". Also, I don't know what you mean by "expected". Amongst many possibilities, you could say:

"... and won Google's prize for 'most important social resource'."

(Of course, if this is a real prize then you have to use the exact same wording as Google do to describe it. I'm not sure if it is, or if you just invented it.)
I'd better stop making up sentences that are just figment of my imagination. Emotion: smile Yes, "nominated" will do the trick, the word expresses precisely what I meant. Thank for your detailed answers, Mr. Wordy.