Basic Ohm's Law is V=IR. The resistors are in parallel so the voltage (V) accross each resistor will always remain constant. Therefore adding more resistors (R) in parallel will only affect the the current (I) going through each resistor.
When you have multiple resistors in parallel, the current will have multiple paths it can take. Current always chooses the path of least resistance so the most dominant resistor in a parallel resistor configuration will be the one with the smallest value. For example: For two parallel reistors, if R1=10Ω, R2= 1MΩ, then Equivalent Resistance (Req) = 9.999Ω.
If the parallel resistors are equivalent, then the current flowing through each resistor will be equivalent as well. For example: If R1=10Ω, R2 = 10Ω, then Req = 5Ω. If V = 10V, using Ohm's Law (V=IR), the current through each resistor will be 1A.