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Aggregation of system-wide information in large-scale distributed systems, such as p2p systems and Grids, can be unfairly influenced by nodes that are selfish, colluding with each other, or are offline most of the time. We present AVCOL, which uses probabilistic and gossip-style techniques to provide availability-aware aggregation. Concretely, AVCOL is the first aggregation system that: (1) implements any (arbitrary) global predicate that explicitly specifies any node's probability of inclusion in the global aggregate, as a mathematical function of that node's availability (i.e., percentage time online); (2) probabilistically tolerates large numbers of selfish nodes and large groups of colluders; and (3) scales well with hundreds to thousands of nodes. AVCOL uses several unique design decisions: per-aggregation tree construction where nodes are allowed a limited but flexible probabilistic choice of parents or children, probabilistic aggregation along trees, and auditing of nodes both during aggregation as well as in gossip-style (i.e., periodically). We have implemented AVCOL, and we experimentally evaluated it using real-life churn traces. Our evaluation and our mathematical analysis show that AVCOL satisfies arbitrary predicates, scales well, and withstands a variety of selfish and colluding attacks.