Roth Conversion - timing & tax consequence

I have determined that it may be beneficial for me to do a Roth Conversion sometime in 2021. What I'd like to avoid is any penalty based on under-payment of taxes.

It is my understanding that taxes in the US is a "pay as you go" system and that if your taxes are under-withheld you can pay a penalty. So, if I make a Roth Conversion late in 2021 it will certainly generate additional taxes owed but am I supposed to have been paying some of that additional tax before the actual conversion was made or does making the additional tax payment based on the conversion at the time of conversion avoid a penalty as I described?

 

Another aspect to the question, is it beneficial to start converting some funds now and pay the taxes on the portion converted rather than lump sum later in the year?