With `sed`:

 sed -e 'x;/^$/,/^*\{3\}/c\' -e ''

That will print only the first paragraph as delimited by an ending blank-line following a line beginning with the string `***`. All intervening lines are squeezed to a single-blank line. That means that while it does not print the `***` for any sequence printed, each paragraph gets a *leading* blank-line - so the first line of output is always blank.

For example:

 sed -e 'x;/^$/,/^*\{3\}/c\' -e '' <<\IN
 blablabla 
 blablabla 
 *** 
 thingsIwantToRead1 
 thingsIwantToRead2 
 thingsIwantToRead3 
 
 blablabla 
 blablabla 
 
 
 blablabla 
 blablabla 
 *** 
 thingsIwantToRead1 
 thingsIwantToRead2 
 thingsIwantToRead3 
 
 blablabla 
 blablabla
 IN

###OUTPUT:

<pre>

thingsIwantToRead1
thingsIwantToRead2
thingsIwantToRead3

thingsIwantToRead1
thingsIwantToRead2
thingsIwantToRead3
</pre>

To avoid that awkwardness, you can do:

 sed -ne '/\n/p;/^*\{3\}/!d;:n' -e 'N;$G;/\n$/D;bn'

...which will print the blanks following a paragraph.

###OUTPUT:

<pre>
thingsIwantToRead1
thingsIwantToRead2
thingsIwantToRead3

thingsIwantToRead1
thingsIwantToRead2
thingsIwantToRead3

</pre>