Forming a personal minyan in shul

A person who came to shul late and did not hear Kaddish, Borchu or Kedusha may daven Pesukei d’Zimrah (together with Yishtabach), and--if there are still nine people in shul--he can then recite Kaddish and Borchu. He should continue until Shemoneh Esrei and say the first three brochos out loud, followed by Kedusha. The poskim disagree about whether he should add L’dor V’dor to the third brocha, which is the nusach for a chazan, or whether he should say Atah Kodosh, which is the nusach for an individual.

סעיף א, ס"ק יג וביה"ל ד"ה ישלם ביאורים ומוספים דרשו 13

When would a person say Borchu before davening?

If a person arrives late but does not think that nine people will wait for him to say the entire Pesukei D’zimrah, he should say a shortened version--consisting of Boruch She’amar, Ashrei and Yishtabach. If people will not even wait for that, he should say a few pesukim and go directly to Kaddish and Borchu. He should then start davening from the beginning. He should not go directly to Shemoneh Esrei in this case, even if it means missing out on Kedusha. If he goes straight to Shemoneh Esrei he will not connect geulah and tefilah, which is more important than Kedusha.

ביה"ל ד"ה שישלים

Can a second minyan start when people from the first minyan are still in shul?

If there is a shul which always has a primary minyan and occasionally a second minyan, the chazan of the second minyan should not stand in the place of the chazan of the first minyan if there are still people remaining from the first minyan. Likewise, they should not start Kriyas HaTorah until everyone from the first minyan leaves. If they begin when people are still there, it will appear as if there was an issue with the first minyan and they were not yotzei. If the shul consistently hosts multiple minyanim, starting a second minyan will not give the impression that there is any issue with the first minyan, and doing so is permissible.  

סעיף א וס"ק טז ו־יח

• Tefilah b’tzibur is when a person davens Shemoneh Esrei together with a minyan of ten men. According to some Achronim, at least ten people must be davening at that time. It is not sufficient to have a situation where most of the ten people are davening but a few non-daveners are there to complete the minyan.

• There is a concept known as pores al Shema. This means that if there are people who did not hear Kaddish, Borchu and Kedusha with the tzibur, they may organize a minyan, appoint a chazan to say Kaddish, Borchu and the brocha of Yotzer Hameoros out loud, immediately followed by the first three brochos of Shemoneh Esrei and Kedusha.

• There is a minhag to repeat Borchu at the end of davening for those who came late. Some congregations say it after Shemoneh Esrei and others say it after the final Kaddish. 

• A woman’s obligation in tefilah

• Does a child have to wake up early to say Kriyas Shema?

• Does a child have to daven?