There are different avatars but Nitai Gaur, they are considered the parama karuna because They were available so freely, They give out the mercy so freely.
Lord Varahadev, He saved the earth, He touched Navadwip dham but somehow the rishis from the higher planets, they saw the gigantic form of Varahadeva. Varahadev shook his back and some water sprinkled on the sages but there wasn’t much chance to serve Him personally.
So we see how Krishna, He made Himself available but that was particular to the Vrajvasis, the wives of the brahmanas who were from the neighboring village and who were not allowed because Lord Krishna said I am playing the part of a vaisya, a cowherd boy and you are brahmanas and we cannot mix. So, it was very hard to approach the Lord. But still if you are fortunate to be born in Vrajdham, then you could. By getting such a birth is a special mercy.
But then we see Lord Caitanya, He travelled, north, south, west of India, for six years and in East Bengal for one year. Each place, He would stay one day and in each house he stayed, the wife would put water on His feet and the husband would massage His feet.
The wife would cook for Him (Lord Caitanya) and the husband would serve the maha prasad and the villagers would gather together and hear some instructions from Lord Caitanya.
Can you figure how many days that was? More than thousands of days! And every day, except for the rainy season, He was at a different house. So like this so many devotees got a chance to serve the Lord directly. There are unlimited ways, but this is one way Lord Caitanya is parama karuna.HH Jayapataka Swami Navadwip Parikrama Lecture March 8th, 2014