Voltage Regulator

To add onto Jenny’s response, it appears you are wondering if there is a minimum load current requirement in order to maintain regulation.

Although some devices have certain load requirements, taking a look at 296-31454-1-ND as an example, would only need to meet the voltage input requirement, which would be output voltage + dropout voltage:

Vout: 3v
Vdropout: 0.6v
Voltage input requirement: 3.6v

For this example, the output will always be regulated to 3v as long as you have a minimum of 3.6v on the input.

Here are a few more articles regarding regulator dropout voltage:

LDO Regulator Selection
Cooling Requirements for Linear Voltage Regulator

Analog Devices
Understand Low-Dropout Regulator (LDO) Concepts to Achieve Optimal Designs

Texas Instruments
Understanding the Terms and Definitions of LDO Voltage Regulators