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In this paper we focus on real situations where certain perfectly divisible estate has to be divided among claimants who can merely indicate the range of their claims, and the available amount is smaller than the aggregated claim. Funds’ allocation of a firm among its divisions, taxation problems, priority problems, distribution of costs of a joint project among the agents involved, various disputes including those generated by inheritance, or by cooperation in joint projects based on restricted willingness to pay, fit into this framework. The corresponding claim of each claimant can vary within a closed interval. For claims and/or estate, intervals are applied whenever the claimants can distinguish the possibility of attaining the amount of estate. Here, a probability interpretation can also be considered, e.g. in taxation problems. We classify the division problems under uncertainty of claims and/or estate and present basic division scheme, which is consistent with the classical bankruptcy proportional rule. Several examples are presented to illustrating particular problems and solution concepts.