Sun-Moon-Mars Conjunction. 

Let's 1st understand what these planets represent on their own?

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses too. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Moon & Mars will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Moon-Mars Conjunction - First of all this conjunction can show someone who is hot headed. It is because Moon, which represents Mind, is with two hot planets, i.e. Sun & Mars. It shows that this person can get angry very soon and can even get violent. If Moon is in between Sun & Mars, then it will take shape of Paap Kartari Yoga as gentle Moon will be crushed by the presence of 2 malefic planets on either side. Otherwise also, this conjunction is not good for Moon as other 2 planets are strong malefics. On positive note, it shows that person can be very hardworking and active as soul & mind both are impacted by Mars. It also shows that parents will infuse lots of courage in person. At the same time, parents can be of dominating nature too. This person can take up professions of the nature of Army, Police, Security or Defense. As it is not a good conjunction for Moon, it means it is not a pleasant situation for Mother of person. She might have faced dominance and anger in her life. This person needs to work really hard to keep his mind at peace and away from aggressive thoughts and actions. Meditation can be of serious help for him. Meditation is not only recommended but necessary for this person. 

Who will win the Conjunction? - As Moon's impact on this conjunction is almost negligible, it shows that this conjunction will largely work because of Sun & Mars. If Mars is combust then surely Sun has higher say till 30 years of age, else we have to decide largely through dignity of Sun & Mars.

Dignity & Strength - 

This conjunction can work best in Aries, Leo, Sagittarius and Pisces as all planets are in good dignity here.

This conjunction can be most challenging in Aquarius as all planets are in weak dignity here. 

In other signs, at least 1 planet will be in good dignity, hence results of the conjunction will largely depend on planets mutual impact on each other, as discussed above, and the dashas.