It is related (Sefer Divrei Dovid) that a large crowd once came to Rav Dovid Moshe of Tchrotkov zy"a with kvitlach. The Rebbe said, "Since there are so many kvitlach, I am forced to do what the Apta Rov zy"a did."
He explained, "One year on Rosh Hashanah and Yom Kippur, the Apta Rov had lots of kvitlach in front of him, and he didn't have enough time to read them all. He took them all and stuffed them into his pockets. He then put his hands on top of his pockets and said, 'I bless all the people who gave me these kvitlach to have children, long life, livelihood, and a good year."
After relating this story, the Tchortkover Rebbe did the same thing. He gathered all the kvitlach into a bag and blessed all the names written on them.